Electricity, Magnetism & Circuits — Print · Physics & Environmental Science, Grade 12

Electric Charge & Fields

Learning goals

• I can explain that charge comes in two types, is quantized, and is conserved.
• I can use Coulomb's law (F = kq₁q₂/r²) to calculate the electrostatic force between two charges.
• I can describe an electric field, calculate it with E = F/q, and sketch its field lines.

Readings for this unit

• A lamp transfers energy while charge keeps circulating

Everything you touch is built from atoms, and buried inside every atom is electric charge. Protons in the nucleus carry positive charge, electrons carry an equal-sized negative charge, and an atom with matching numbers of each is electrically neutral. Charge is quantized — it always comes in whole-number multiples of the elementary charge, e = 1.6 × 10⁻¹⁹ coulombs — so you can strip away three electrons or add a thousand, but never half of one. Charge is also conserved: it is never created or destroyed, only moved from one object to another. When you rub a balloon on your hair, you are not making charge, just transferring electrons from the hair to the balloon.

The single most important rule of charge is short: like charges repel, and opposite charges attract. Two negatives push apart, two positives push apart, but a positive and a negative pull together. This is strikingly different from gravity, which only ever attracts — electric forces come in both flavors, and that two-sidedness is exactly what makes circuits, chemistry, and electronics possible. It also explains everyday static electricity: a comb that has stolen electrons becomes negatively charged and can lift tiny bits of paper by attracting their positive regions.

Conductors have charge carriers that can move through the material under suitable conditions. Ordinary insulators strongly restrict sustained charge conduction but can still polarize, accumulate surface charge, leak, or break down at sufficiently large fields. Conducting versus insulating behavior depends on material, temperature, and operating conditions; it is not a claim that every electron is perfectly fixed or that an arbitrary insulating layer guarantees safe handling.

To go beyond 'they attract or repel' and actually predict the force, we use Coulomb's law: F = k·q₁·q₂ ÷ r², where the charges are in coulombs, the distance r is in meters, and the constant k ≈ 9 × 10⁹ N·m²/C². Two features matter most. Bigger charges mean a bigger force, in direct proportion. And because r is squared in the denominator, the force falls off fast with distance — double the separation and the force drops to a *quarter*, triple it and the force drops to a *ninth*. This inverse-square shape is the exact same mathematical fingerprint that Newton's law of gravitation carries, which is why the two laws are so often taught side by side.

An electric field describes local force per sufficiently small positive test charge, E=F/q, in N/C. A source produces a field whether or not that test is present, and a negative test feels force opposite E. Field lines point away from positive and toward negative sources; their density can encode relative magnitude under a consistent drawing convention. Approximately uniform parallel-plate fields apply away from edge effects. Changes in sources propagate physically rather than implying instantaneous influence across arbitrary distances.

These ideas are the bedrock of the entire unit and of modern technology. A moving stream of charge is nothing more than an electric current, the subject of the next lesson, and the push that drives it is a difference in electric potential built from these very fields. Electric fields steer the electrons that paint an old TV screen, sort the toner in a laser printer, trigger the spark in an engine, and register the touch of your finger on a phone. Learn to reason about charge, Coulomb's law, and fields, and you hold the key that unlocks everything from a single spark to the power grid.

Model check: Field exists as a model independent of the particular small test charge. F=qE=.002N along the field; a negative charge would reverse direction.

Coulomb's Law

F = k·q₁·q₂ ÷ r²

F is the electrostatic force in newtons (N); q₁ and q₂ are the charges in coulombs (C); r is the separation in meters (m); k ≈ 9 × 10⁹ N·m²/C².

Electric Field Strength

E = F ÷ q

E is the electric field in newtons per coulomb (N/C); F is the force on a small test charge q. For a point charge this also equals E = k·q ÷ r².

Worked examples

Avoid these mistakes

• Field exists as a model independent of the particular small test charge.

Words to know

electric charge

A fundamental property of matter that comes in two types, positive and negative, measured in coulombs (C).

Coulomb's law

The rule that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance: F = kq₁q₂/r².

electric field

The region around a charge where another charge would feel a force; its strength is the force per unit charge, E = F/q, in N/C.

conductor

A material such as copper in which some electrons are free to move, so charge flows through it easily.

insulator

A material such as rubber or glass whose electrons are locked in place, so charge does not flow through it.

Coulomb weighed an invisible force with a twisted thread

How do you measure a force too weak to feel? In 1785, French engineer Charles-Augustin de Coulomb built a torsion balance: a light rod hung from a thin fiber, with a charged ball on one end. Bringing a second charged ball nearby made the rod twist, and the amount of twist revealed the force with astonishing precision. By varying the charges and distances, Coulomb showed the force is proportional to the product of the charges and falls off as the square of the distance — the inverse-square law we now write F = kq₁q₂/r². The unit of charge, the coulomb, is named in his honor, and the same delicate torsion-balance trick was later used to weigh the gravitational constant.

You can't have half an electron: Millikan's oil drops

The idea that charge is quantized — that it comes only in whole multiples of a smallest unit — was nailed down between 1909 and 1913 by Robert Millikan in his famous oil-drop experiment. He sprayed tiny charged oil droplets between two charged plates and balanced gravity against the electric force to measure the charge on each drop. Every charge he found turned out to be a whole-number multiple of the same tiny value, e ≈ 1.6 × 10⁻¹⁹ coulombs — the elementary charge. There simply were no in-between values. This is why you can transfer one electron or a billion, but never a fraction of one, and it earned Millikan the 1923 Nobel Prize in Physics.

Coulomb's law and Newton's gravity: identical shape, wildly different strength

Look at Coulomb's law and Newton's law of gravitation side by side and they are mathematical twins — both are inverse-square laws where the force depends on the product of two 'source' quantities (charge for one, mass for the other) divided by distance squared. But their strengths are worlds apart: between two electrons, the electric repulsion is about 10⁴² times stronger than their gravitational attraction. So why does gravity rule planets and galaxies while electricity seems to hide? Because matter is almost perfectly neutral — equal positive and negative charge cancel out over any large object — while mass only ever adds up. Gravity wins the cosmos by default, simply because charge cancels and mass never does.

Lightning is charge separation on a colossal scale

A thundercloud is a Coulomb's-law laboratory kilometers tall. Violent updrafts and colliding ice particles strip electrons from one region and pile them into another, separating enormous amounts of charge and building potential differences of hundreds of millions of volts between cloud and ground. When the electric field grows strong enough to rip electrons off air molecules, the air suddenly becomes a conductor and a lightning bolt discharges it all in a few thousandths of a second. Benjamin Franklin's famous (and extremely dangerous) 1752 kite work argued that lightning was simply electricity, and led directly to the lightning rod — a pointed conductor that quietly bleeds charge away and gives a strike a safe path to ground.

In the real world

Laser printers and photocopiers use Coulomb's law in action: a charged drum attracts oppositely charged toner powder exactly where the image should appear, then presses it onto the paper.

Exit check

A+2microC test charge in 1000N/C field experiences what force?

Current, Voltage & Resistance

Learning goals

• I can define electric current as the rate of flow of charge and calculate it with I = Q/t.
• I can explain voltage as the energy delivered per unit of charge, using V = W/Q.
• I can describe resistance and the wire properties that increase or decrease it.

Readings for this unit

• A lamp transfers energy while charge keeps circulating

In the last lesson charges sat still; now we set them marching. Electric current is simply the rate at which charge flows past a point in a circuit, written I = Q ÷ t — the amount of charge Q, in coulombs, divided by the time t, in seconds. Its unit is the ampere (A), and one amp means one full coulomb of charge (about 6.2 × 10¹⁸ electrons) streaming past every second. By long-standing convention we describe current as flowing from the positive terminal of a battery to the negative one, even though in a metal wire it is actually the negative electrons drifting the opposite way.

Potential difference, or voltage, is energy per charge between two points, in J/C. A steady ideal 9 V source supplies 9 J per coulomb crossing its rise. In an ordinary resistive circuit an electric field supports charge drift, but induction and other devices require their own source model; “voltage always causes current” is not a universal definition. An open circuit can have voltage with almost no steady current, and charge-flow rate also depends on the actual network and operating conditions.

The third member of the trio is resistance, the opposition a material offers to the flow of charge, measured in ohms (Ω). As charge pushes through a material, it collides with the vibrating atoms of the lattice and loses energy, which is why a resistor warms up. Resistance is what converts electrical energy into the heat of a toaster, the glow of a bulb filament, and the warmth of a hair dryer — all deliberately built to resist current so that the energy shows up as heat and light.

For an ideal uniform ohmic wire, R=ρL/A, so a longer wire increases resistance and a larger cross-sectional area reduces it when material and conditions remain fixed. Resistivity depends on material and temperature. Many metals increase in resistivity as they warm, but semiconductors and other materials can behave differently. The long-thin-hot ranking is therefore a conditional metal-wire example, not a universal law for every conductor.

The classic way to feel how these three quantities relate is a water-pipe analogy. Picture water pumped around a loop of pipe: the voltage is like the pressure from the pump that pushes the water, the current is like the amount of water actually flowing past each second, and the resistance is like a narrow, constricted section of pipe that holds the flow back. Raise the pressure (voltage) and more water flows; pinch the pipe tighter (more resistance) and less water flows. The analogy is not perfect, but it captures the essential cause-and-effect: voltage pushes, resistance restrains, and current is the flow that results.

These three ideas — current, voltage, and resistance — are the vocabulary of every electrical device on Earth, and they do not act independently. Push harder (more voltage) and current rises; add more resistance and current falls. That precise relationship is captured by Ohm's law, the centerpiece of the next lesson, which ties all three together into a single equation you can solve. Master what current, voltage, and resistance each *mean* here, and Ohm's law becomes not a formula to memorize but a sentence you already understand.

Model check: Current does not mean charges are consumed; a component transfers energy while charge is conserved. I=Q/t=3 A; conventional current direction is positive-charge flow.

Electric Current

I = Q ÷ t

I is current in amperes (A); Q is charge in coulombs (C); t is time in seconds (s). One amp is one coulomb per second.

Voltage (Potential Difference)

V = W ÷ Q

V is voltage in volts (V); W is the energy in joules (J) given to charge Q in coulombs (C). One volt is one joule per coulomb.

Worked examples

Avoid these mistakes

• Current does not mean charges are consumed; a component transfers energy while charge is conserved.

Words to know

electric current

The rate at which electric charge flows past a point, I = Q/t, measured in amperes (A).

ampere (A)

The SI unit of current; one ampere is one coulomb of charge flowing per second.

voltage (potential difference)

The electrical energy delivered to each unit of charge, V = W/Q, measured in volts (V).

resistance

The opposition a material offers to the flow of current, measured in ohms (Ω).

resistivity

A property of a material itself that sets how strongly it resists current; it, along with a wire's length and thickness, determines the wire's resistance.

Twitching frog legs and the first battery

In the 1780 s, Italian anatomist Luigi Galvani noticed that a dead frog's leg twitched when touched by two different metals, and concluded he had found a mysterious 'animal electricity.' His countryman Alessandro Volta disagreed — he suspected the electricity came from the metals themselves, not the frog. To prove it, in 1800 Volta stacked alternating discs of zinc and copper separated by brine-soaked cloth and produced the first steady source of current in history: the voltaic pile, the ancestor of every battery. Volta was right, and the debate gave us a lasting reward — the unit of voltage, the volt, is named after him, while Galvani's name survives in 'galvanized' metal and the galvanometer.

Electrons crawl, but the signal flies

Flip a switch and a lamp across the room lights instantly, which makes it tempting to think electrons race through the wire near light speed. They don't. The actual drift velocity of electrons in a typical wire is astonishingly slow — often less than a millimeter per second, slower than a snail. What travels fast is the electric field that pushes them: it propagates through the wire at close to the speed of light, nudging electrons everywhere into motion almost at once. Picture a tube already packed with marbles — push one in at your end and a marble instantly pops out the far end, even though no single marble made the whole trip. The 'push' is fast; the marbles themselves barely move.

Superconductors: when resistance drops to exactly zero

Resistance usually rises with temperature, so what happens if you go the other way and make a material extremely cold? In 1911, Dutch physicist Heike Kamerlingh Onnes cooled mercury to about 4 kelvin (−269 °C) and watched its electrical resistance vanish — not just shrink, but drop to exactly zero. A current started in a loop of superconductor can circulate for years without a battery, because nothing dissipates its energy. Today superconductors wind the powerful electromagnets inside MRI scanners and maglev trains, and one of physics' great quests is to find a material that superconducts at everyday temperatures, which would transform how the world moves electricity.

AC vs DC: the War of the Currents

In the 1880 s and 1890 s, Thomas Edison championed direct current (DC), while George Westinghouse and Nikola Tesla backed alternating current (AC) — a rivalry so fierce it became known as the War of the Currents. AC won, and the reason is pure physics. Power lost as heat in a transmission line is P = I²R, so to ship power across long distances with low loss you want very low current and very high voltage. Transformers can step AC voltage up for transmission and back down for safe home use, but they only work on changing (alternating) current — which is exactly why the grid outside your window hums along at AC, while the battery in your phone stores DC.

In the real world

Every device you plug in is rated for a certain voltage and draws a certain current; electricians use these numbers to choose wires thick enough that their resistance won't overheat them.

Exit check

24C passes in 8 s. Find current.

Circuits & Ohm's Law

Learning goals

• I can apply Ohm's law (V = IR) to find voltage, current, or resistance in a circuit.
• I can find the total resistance of resistors wired in series and in parallel.
• I can calculate electrical power with P = IV and relate it to energy used.

Readings for this unit

• A lamp transfers energy while charge keeps circulating

The three quantities from the last lesson lock together in the most useful equation in all of electronics, Ohm's law: V = I × R. Voltage equals current times resistance, and the same relationship rearranges to I = V ÷ R and R = V ÷ I, so knowing any two of the three always gives you the third. Read it as a story: for a fixed battery voltage, piling on more resistance chokes the current down, while lowering the resistance lets more current surge through. A resistor that obeys this straight-line relationship at constant temperature is called 'ohmic,' and it is the assumption behind almost every circuit calculation you will do.

How the components are wired matters just as much as their values. A series circuit offers just one single loop for charge to travel, so the very same current flows through every component in turn. Because the charge must pass through each resistor one after another, their resistances simply add up: R_total = R₁ + R₂ + R₃ + …, and the total is always larger than any single resistor. The voltage from the battery divides among them, with the biggest resistor taking the biggest share. The weakness of a series circuit is its single path — break it anywhere and the current stops everywhere, which is why one dead bulb once darkened an entire old string of holiday lights.

A parallel circuit gives charge several branches to choose from at once. Here every branch is connected across the same two points, so each one receives the full battery voltage, and the branch currents add up to the total. Counterintuitively, adding more parallel branches *lowers* the overall resistance, because you are opening more lanes for charge to flow: 1 ÷ R_total = 1 ÷ R₁ + 1 ÷ R₂ + …, giving a total that is always smaller than the smallest branch. For just two resistors this tidies up to R = R₁R₂ ÷ (R₁ + R₂). This independence is why your home is wired in parallel — you can switch off one lamp, or have one appliance fail, without cutting power to everything else.

Many resistor networks can be simplified through series and parallel groups, but a bridge network may require general node and loop equations instead. Series/parallel formulas assume ideal wires and the stated component behavior. Real devices can contain capacitors, inductors and nonlinear elements, so a constant-R calculation does not predict every transient or arbitrary appliance. Trace topology, identify conditions and then choose an appropriate method.

Circuits exist to *do* something, and that means converting electrical energy into other forms — light, heat, motion, sound. The rate of that conversion is electrical power, P = I × V, measured in watts, where one watt is one joule of energy converted per second. Combine it with Ohm's law and it takes two other handy forms, P = I²R and P = V² ÷ R, letting you find power from whichever two quantities you know. A 60-watt bulb converts 60 joules of electrical energy every second; multiply a device's power by the time it runs and you get the total energy it uses, which is exactly what your utility meters and bills.

Together, Ohm's law, series and parallel rules, and the power equation let you predict a circuit completely — how much current each part draws, how the voltage splits up, and how much energy is consumed and where. That predictive power is not academic: it is how a fuse or circuit breaker is sized to trip before too much current overheats the wiring, how a phone charger is designed to deliver exactly the right current, and how engineers keep the enormous circuit of the electrical grid balanced. Build a real device and these are the rules you will actually reach for.

Model check: A series circuit has equal current; a parallel circuit has equal branch voltage. 1/R=1/6+1/6=1/3, soR=3ohm; lower than either branch.

Ohm's Law

V = IR

V is voltage in volts (V); I is current in amps (A); R is resistance in ohms (Ω). Rearranges to I = V ÷ R and R = V ÷ I.

Series Resistance

R = R₁ + R₂ + R₃ + …

resistances in series simply add; the total is always larger than any single resistor.

Parallel Resistance

1 ÷ R = 1 ÷ R₁ + 1 ÷ R₂ + …

for resistors in parallel; the total is always smaller than the smallest single resistor. For two, R = R₁R₂ ÷ (R₁ + R₂).

Electrical Power

P = IV

P is power in watts (W); I is current in amps (A); V is voltage in volts (V). Can also be written P = I²R or P = V² ÷ R.

Worked examples

Avoid these mistakes

• A series circuit has equal current; a parallel circuit has equal branch voltage.

Words to know

Ohm's law

The relationship V = IR linking voltage, current, and resistance for a resistor at constant temperature.

series circuit

A circuit with a single path, so the same current flows through every component and their resistances add.

parallel circuit

A circuit with two or more branches, so each branch has the full voltage and the total resistance is less than any one branch.

equivalent resistance

The single resistance that could replace a whole combination of resistors and draw the same current.

electrical power

The rate at which a device converts electrical energy, P = IV, measured in watts (W).

Georg Ohm was ridiculed before he was revered

When German schoolteacher Georg Simon Ohm published his law relating voltage, current, and resistance in 1827, the reception was chilly — some colleagues dismissed the work as unscientific fantasy, and it cost him professionally for years. Time proved him spectacularly right: V = IR became one of the most-used equations in all of engineering, and the SI unit of resistance, the ohm (Ω), now carries his name. It's a useful reminder that even a relationship that looks obvious in hindsight can take a generation to be accepted, and that careful measurement eventually wins the argument.

Ohm's 'law' isn't actually a law of nature

It's easy to assume V = IR always holds, but it's really a property that only some materials happen to obey, and only under steady conditions. A device where current stays proportional to voltage is called ohmic — a plain resistor at constant temperature is the classic example. Plenty of everyday components are non-ohmic: a light-bulb filament's resistance climbs sharply as it heats up, so doubling the voltage does not double the current, and a diode conducts freely in one direction but blocks the other, giving a wildly curved voltage-current graph. Ohm's law is an excellent model within its limits, not an ironclad rule of the universe.

Kirchhoff's rules and why your house is wired in parallel

For circuits too tangled for a single series-or-parallel shortcut, Gustav Kirchhoff gave two bookkeeping rules in 1845. His current law says all the current flowing into any junction must equal the current flowing out (charge can't pile up). His voltage law says the voltage changes around any complete loop must sum to zero (energy per charge returns to where it started). These rules explain why homes are wired in parallel: every outlet connects across the same two supply lines, so each receives the full 120 V independently, and switching one device off doesn't starve the rest — a series house would go completely dark the moment any single bulb failed.

The kilowatt-hour and where your electric bill comes from

Electrical power is P = IV, measured in watts, but your utility bills you for energy, which is power multiplied by time. The everyday unit is the kilowatt-hour (kWh) — the energy used by 1,000 watts running for one hour, equal to 3.6 million joules. A 1,500-watt space heater running for 4 hours uses 1.5 kW × 4 h = 6 kWh; at, say, 15 cents per kWh, that's about 90 cents. This is also why high-power appliances like ovens and dryers get their own dedicated, thick-wire circuits: P = IV means high power at household voltage demands a large current, and only a thick wire can carry that current without its own resistance overheating it.

In the real world

Your home is wired in parallel so each outlet gets the full 120 V, and a circuit breaker watches the total current — using P = IV, an electrician can predict when too many high-power appliances on one circuit will trip it.

Exit check

Two 6ohm resistors in parallel have what equivalent R?

Magnetism & Electromagnetism

Learning goals

• I can describe magnetic fields, poles, and the force between magnets.
• I can explain how an electric current creates a magnetic field and calculate the force on a wire with F = BIL.
• I can explain electromagnetic induction and how motors and generators convert energy.

Readings for this unit

• A lamp transfers energy while charge keeps circulating

Magnets are familiar, but their behavior sets the stage for the deepest idea in the unit. Every magnet has two poles, north and south, and the rule mirrors electric charge: like poles repel, opposite poles attract. Around every magnet stretches a magnetic field, an invisible region of influence we draw with field lines running out of the north pole and into the south. Unlike electric charges, you can never isolate a single pole — snap a bar magnet in half and each piece instantly has its own north and south. Earth itself is one giant magnet, and its field is what swings a compass needle to point north.

For centuries electricity and magnetism looked like separate subjects, until 1820, when Hans Christian Oersted noticed a compass needle twitch every time he switched on a nearby electric current. That tiny deflection was a revelation: an electric current produces a magnetic field. Coil that current-carrying wire into a loop, or many loops, and the magnetic fields reinforce into a strong, controllable magnet — an electromagnet. Because it works only while current flows, an electromagnet can be switched on and off and made stronger simply by adding more turns or more current, which is exactly why scrapyard cranes, doorbells, and hard drives rely on them instead of permanent magnets.

A straight current-carrying wire segment in a uniform field has magnetic-force magnitude BIL sinθ, where θ is the angle between current direction and field. The simpler BIL applies when they are perpendicular. Direction follows the appropriate vector rule, and force can be zero for a parallel segment. Magnetic interactions can exert torque on a coil in a motor, with electrical input, motion, and losses included in the energy account.

Faraday’s law relates induced emf to the rate of change of magnetic flux linked with a circuit. Flux can change through field strength, loop area, or orientation. A stationary loop in a steady field has no induction from that unchanged flux. Sustained induced current additionally requires a conducting path and appropriate circuit behavior; an open loop can have emf without a closed-path current. Lenz’s law relates the response direction to the flux change.

A generator can convert mechanical input into electrical transfer by changing linked magnetic flux. Rotation in a field can change flux through a coil even when the external field is steady. Turbine-driven generators are used in many thermal, wind, and hydro systems; photovoltaics produce electricity by a different mechanism. Track actual energy inputs and outputs instead of describing every electrical source as induction or imagining newly created electrons delivered from the generator.

Electric and magnetic effects are parts of electromagnetism. Electric currents and changing fields can produce magnetic fields; changing magnetic flux linked with a circuit produces emf under the stated conditions. Current additionally requires the relevant conducting path and circuit response. Maxwell’s field framework also supports electromagnetic waves. This connected account does not mean every static field automatically generates a current or provides a new energy source.

Model check: A static magnet beside a stationary coil does not continuously generate emf. A changing magnetic flux, through changing field, area, or orientation; a moving magnet can supply that change.

Build your understanding

Use the detailed parent plan: two core 50–60-minute sessions per focused unit, with a third assigned for selected calculation/modeling topics. First study the core explanation and Parts 1–2 with their figures/checks; next study Parts 3–4, the whole-unit application, worked cases, varied practice and exit check. Attempt reasoning before opening guidance. Extend time when actual understanding requires it; investigations and chapter assessments have separate sessions.

Part 1 · Distinguish magnetic interactions from charge signs

A bar magnet has north and south magnetic poles, not a separated pair of ordinary positive and negative electric charges. External field directions run from north toward south, while complete magnetic field lines continue through the magnet as closed loops. Cutting an ordinary magnet produces smaller dipoles rather than an isolated electric charge at each cut. A field-line drawing summarizes direction and relative pattern, not a set of material threads.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

Does a north pole mean a positively charged end?

Visual reasoning — after your attempt

No. Magnetic pole labels and net electric charge are different properties.

Magnetic poles and electric charge signs are different organizing concepts. Ordinary bar magnets have north and south poles; breaking one does not isolate an ordinary single pole. Magnetic field lines describe field direction, and their pattern is not a set of physical threads.

A compass aligns approximately with the local field subject to other interactions. Nearby current and magnetic materials can alter the pattern.

Pause and explain

Does a north magnetic pole mean positive electric charge?

Check your reasoning after answering

No. Magnetic poles and electric charges describe different properties and must not be substituted for each other.

Part 2 · Use magnetic force direction and magnitude

For a moving charge, magnetic force is F=q(v×B), with magnitude |q|vBsinθ. The cross product gives a perpendicular direction by the right-hand rule for positive q; a negative charge reverses it. Here velocity is right and field is out of the page, so positive-charge force is down. A stationary charge has no magnetic force in this simple expression, although an electric field can still act on it.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

If the moving charge is negative, which way is its magnetic force in this diagram?

Visual reasoning — after your attempt

Up. Reversing q reverses the force from the positive-charge right-hand result.

For a moving charge, magnetic force magnitude is |q|vB sinθ and direction is perpendicular to velocity and field, with charge sign included. The magnetic force alone does no work on a point charge because it is perpendicular to instantaneous velocity. Electric forces can still transfer energy.

A charge moving parallel to a uniform magnetic field has zero magnetic force even though the field is present.

Pause and explain

Can a magnetic field alone speed up a point charge through this force?

Check your reasoning after answering

Not through the qv×B force alone; it can change direction but its perpendicular force does no work in this model.

Part 3 · Separate flux from field magnitude

Magnetic flux measures the field passing through an oriented surface. For a uniform field and flat area, ΦB=BAcosθ, where θ is between B and the area normal, not the surface itself. A loop can have nonzero field but zero net flux when its plane is parallel to B. Flux is measured in webers and differs from field strength in teslas. Changing field, loop area or orientation can change flux.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

What flux results if B lies parallel to the loop plane?

Visual reasoning — after your attempt

Zero for a uniform field and flat loop, because θ=90° from the area normal.

Magnetic flux through a flat area is BA cosθ for a uniform field, with θ between field and the area’s normal. Flux changes if field, area, or orientation changes. A strong field does not necessarily give large flux through a surface oriented parallel to it.

Rotating a loop changes its area orientation and can change flux even with fixed B. A drawing should label the normal rather than the surface angle.

Pause and explain

Why can nonzero B give zero flux through a flat loop?

Check your reasoning after answering

If the field is perpendicular to the area normal, cosθ=0; the field lies along the surface rather than crossing it.

Part 4 · Use induction as a change and energy account

Electromagnetic induction produces an emf associated with changing magnetic flux: ε=−NΔΦB/Δt for the stated coil model. Emf is energy supplied per charge around a circuit; a current also needs a closed conducting path. Lenz’s law expresses the opposing sign: the induced response resists the flux change. Mechanical work or another external energy input supplies the electrical output, so a stationary magnet beside an unchanged coil does not provide endless electrical power.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

A 100-turn coil changes flux per turn by 0.002 Wb in 0.10 s. Find average emf magnitude.

Visual reasoning — after your attempt

|ε|=100×0.002/0.10=2 V; its direction needs the geometry and sign convention.

Faraday’s law relates induced emf to flux-change rate, and Lenz’s law gives a direction opposing the change that produces it. An induced current requires a conducting path and depends on resistance and other circuit behavior. Induction does not supply unlimited energy without a source.

A changing-field or moving-loop arrangement needs an energy input account. The opposition implied by Lenz’s law is consistent with energy conservation.

Pause and explain

Does induced emf alone determine induced current?

Check your reasoning after answering

No. Current also depends on the circuit path, resistance, and dynamic behavior; an open loop can have emf without sustained closed-path current.

Apply the whole unit · Calculate an ideal induced emf

Illustrative 200-turn coil has flux per turn decrease uniformly from 0.00500 Wb to 0.00100 Wb in 0.100 s. Total closed-circuit resistance is 4.00 Ω; neglect inductive transients.

Your task

Find emf magnitude and approximate current, explain the Lenz-law direction qualitatively, and identify why a flux decrease alone does not specify clockwise versus counterclockwise.

What your response should show

• Define the system, quantities, units, and relevant conditions before selecting a model.
• Show intermediate calculations or a labeled evidence account, including signs or denominators.
• Explain how the supplied evidence supports the conclusion rather than reporting only an answer.
• Identify a meaningful uncertainty, model limit, or measurement needed to test the conclusion.

Response guidance — after your attempt

1. Flux change per turn is −0.00400 Wb over 0.100 s.

2. Emf magnitude=N|ΔΦ|/Δt=200×0.00400/0.100=8.00 V.

3. Approximate current magnitude=8.00/4.00=2.00 A.

The induced magnetic response tends to oppose the decrease in flux. A clockwise or counterclockwise label additionally needs the field direction, viewing side, and coil orientation. Current uses the stated resistance and negligible-transient approximation; an actual coil can need a fuller time-dependent account.

Scientific references and source-model foundations

• OpenStax — series and parallel circuits
• OpenSciEd 8.3 — forces at a distance
• OpenSciEd public middle-school figure license — CC BY 4.0

Parent / teacher teaching notes

Ask for the direction of the flux change before the current direction. Require a viewing convention and distinguish induced emf from a guaranteed current. Ask the learner to explain each symbol, axis, unit and arrow before calculating. Calculated examples, supplied illustrative records and actual historical observations are labeled separately. Selected public OpenSciEd middle-school source figures are foundation examples, not complete high-school editions or an endorsement; all advanced explanations are supplied locally.

Force on a Current-Carrying Wire

F = BIL

F is force in newtons (N); B is magnetic field strength in tesla (T); I is current in amps (A); L is the length of wire in the field in meters (m).

Worked examples

Avoid these mistakes

• A static magnet beside a stationary coil does not continuously generate emf.

Words to know

magnetic field

The region around a magnet or current where magnetic forces act, measured in tesla (T) and drawn with field lines from north to south.

electromagnet

A magnet created by running electric current through a coil of wire, often around an iron core, that can be switched on and off.

electromagnetic induction

The production of a voltage (and current) in a conductor by a changing magnetic field.

electric motor

A device that uses the force on a current-carrying wire in a magnetic field to convert electrical energy into motion.

generator

A device that uses electromagnetic induction to convert mechanical motion into electrical energy — essentially a motor run in reverse.

A twitching compass and an iron ring: the unification begins

In April 1820, Danish physicist Hans Christian Oersted was lecturing when he noticed a compass needle deflect every time he switched on a nearby electric current — the first hard evidence that electricity and magnetism are connected. Eleven years later, England's Michael Faraday wound two coils on opposite sides of an iron ring and found that switching current on or off in one coil induced a momentary current in the other, with nothing but the changing magnetic field connecting them. Oersted showed current makes magnetism; Faraday showed changing magnetism makes current. Together, these two discoveries opened the door to the electric age.

Magnetism is electricity seen in motion

Here is one of the strangest and most beautiful ideas in physics: electric and magnetic fields are not two separate things but two views of a single electromagnetic field, and which one you see depends on your motion. A stationary charge produces only an electric field; set it moving and a magnetic field appears alongside it. In fact, the magnetic force between two current-carrying wires can be re-described, from a frame moving with the charges, as an ordinary electric force — the two are linked by Einstein's special relativity. It's no accident that his landmark 1905 paper was titled 'On the Electrodynamics of Moving Bodies'; the deep unity of electricity and magnetism was one of the puzzles that led him straight to relativity.

Almost all the world's electricity is Faraday's induction

Step back and the scale of Faraday's 1831 discovery is staggering: the overwhelming majority of electrical energy generated on Earth comes from electromagnetic induction — spinning coils or magnets to induce a current. A coal or gas plant burns fuel only to boil water into steam whose single purpose is to spin a turbine; a nuclear plant uses fission heat to do the very same thing; hydroelectric dams and wind farms spin the turbines directly with moving water or air. In every case, the final step that actually makes the electricity is a magnet and a coil in relative motion. The notable exception is the solar panel, which makes current directly from light with no moving parts at all — but even it feeds into a grid built entirely around induction.

Motors, maglev, MRI, and the data on your hard drive

Once you can turn electricity into magnetism and back, electromagnetism quietly runs modern life. Electric motors — using the F = BIL force on a current-carrying coil — spin everything from kitchen blenders and washing machines to the wheels of electric cars. Maglev trains float and glide on carefully controlled electromagnets, eliminating wheel friction entirely. MRI scanners use enormous superconducting electromagnets to image the inside of your body without any radiation. And for decades, computer hard drives stored every file as microscopic patterns of magnetization, written and read by tiny electromagnetic heads. Behind each of these is the same two-way street Oersted and Faraday discovered: current makes magnetism, and changing magnetism makes current.

In the real world

Nearly all the world's electricity comes from generators: power plants spin turbines — with steam, wind, or falling water — to turn coils inside magnetic fields, using Faraday's induction to push current to your home.

Exit check

What induces emf in a stationary coil?

Electric Potential, Potential Energy & Capacitors

Learning goals

• I can distinguish electric potential, field, and potential energy.
• I can calculate capacitor charge and energy with unit-prefix conversions.

Readings for this unit

• A lamp transfers energy while charge keeps circulating

Electric field is force per unit positive test charge: E=F/q. Electric potential is potential energy per unit charge, V=U/q, measured in joules per coulomb. A field is a vector, while potential is scalar. Voltage means potential difference between two locations, not a substance flowing through wire.

When a charge q moves across potential difference ΔV, its electric potential-energy change is ΔU=qΔV. Positive and negative charges respond differently to the same voltage sign. If the electric field alone does work, Welectric=−ΔU. An outside agent moving charge slowly can do positive work to increase U.

In an approximately uniform electrostatic field, potential decreases along the field: ΔV=−E·Δr. For a displacement distance d along the field, ΔV=−Ed and the magnitude is Ed. Equipotential surfaces have constant potential and are perpendicular to the local nonzero field. This simple relation must not replace a geometry-dependent nonuniform-field calculation.

A capacitor stores separated charge and energy. Capacitance C=Q/ΔV depends on geometry and dielectric material in a linear model; capacitance units are farads. Use Csymbol carefully because the letter C is also used for the coulomb unit. A simple parallel-plate model gives C=εA/d.

Stored capacitor energy is U=½C V²=½QV=Q²/(2C). The half arises because voltage rises as charge accumulates. Doubling voltage quadruples energy for fixed capacitance. Charge is not consumed when the capacitor releases energy; charges redistribute.

Use paper calculations with small unit scales. Capacitors from electronics can retain hazardous energy even after unplugging; do not dismantle appliances or discharge unknown equipment. A concept diagram provides the necessary model without handling stored-energy devices.

Worked examples

Avoid these mistakes

• Voltage does not flow; current is the rate of charge transfer.

Words to know

electric potential

Electric potential energy per unit charge.

capacitance

Charge stored per potential difference in a linear model.

equipotential

A surface or set of points at equal electric potential.

In the real world

Use the chapter investigation to connect this unit to measured evidence and a practical decision.

Exit check

What does 9 V mean in energy terms?

Electrical Power, Energy & Circuit Design

Learning goals

• I can calculate component power and energy with correct circuit values.
• I can distinguish efficiency, kilowatt-hours, and source internal losses.

Readings for this unit

• A lamp transfers energy while charge keeps circulating

Electrical power is energy-transfer rate. For a component with voltage V and current I, P=VI. An ohmic resistor also gives P=I²R=V²/R because V=IR. A device’s actual resistance can depend on temperature; not every electronic component follows a constant-R model.

Electrical energy transferred over a constant-power interval is E=Pt. The kilowatt-hour is an energy unit: 1 kWh=1000W×3600 s=3.60×10⁶ J. It is not a kilowatt per hour. A household bill can be modeled from energy amount times a supplied price per kWh, but real tariffs include other charges.

In a series circuit, current is the same through components and voltage drops add; in parallel, each branch has the same potential difference and branch currents add. Power calculations must use each component’s own voltage or current, not indiscriminately the supply total.

Batteries have internal resistance. In a simple discharging model, terminal voltage V=emf−Irinternal, and internal heating is I²rinternal. A short circuit can cause a large current and dangerous heating; a battery is not an unlimited constant-voltage source at all loads.

A practical design specifies required function, maximum current, operating duration, and energy capacity. Efficiency compares useful output with electrical input. Different lamps can use different powers for similar useful illumination; comparison should specify light output and lifetime rather than watts alone.

Build only low-voltage circuits with an appropriate educational kit and adult guidance; never use wall sockets, improvised mains wiring, or short a battery. Heating-appliance examples below are paper problems. Circuit calculations do not substitute for equipment ratings or electrical installation knowledge.

Worked examples

Avoid these mistakes

• Watts measure power; watt-hours and joules measure energy.

Words to know

kilowatt-hour

Energy delivered by 1 kW over 1hour, equal to 3.60MJ.

internal resistance

A simplified source resistance causing voltage drop and heating.

emf

Source energy per charge under the modeled open-circuit condition.

In the real world

Use the chapter investigation to connect this unit to measured evidence and a practical decision.

Exit check

How would you compare two lamp designs fairly?