Magnetism and Electromagnetism

Four topics on a field that only notices things that move. Magnetic fields as closed loops with no monopole to start on, the force on a moving charge, perpendicular to both the velocity and the field and therefore doing no work, current-carrying wires that circle a field around themselves and then push on each other, and induction, where a changing flux drives a current that resists the change.

AP exam 12-15%4 topics

Topics

12.1

Magnetic Fields

Magnetism and Moving Charges

Magnetism and Current-Carrying Wires

Electromagnetic Induction and Faraday's Law

Lesson

Diagnostic

after diagnostic

Key forms For every problem in this unit

Field lines

CLOSED loops: north to south outside a magnet, south to north inside it. No monopole, so a line never begins or ends

Cutting a magnet

every piece is a complete dipole. The magnetism comes from circulating charge, not from magnetic charge at the tip

A compass

aligns TANGENT to the local field line, not aimed at the nearest pole

Force on a moving charge

F = qvB sinθ, θ between v and B. Zero if v = 0 or v is PARALLEL to B

Its direction

PERPENDICULAR to both v and B, by the right-hand rule. Reverse the result for a negative charge

Work done

ZERO, always. A perpendicular force turns the velocity and never changes the speed

Circular path

qvB = mv²/r, so r = mv/(qB). Faster means a BIGGER circle; stronger B means a tighter one

Field of a long straight wire

B = μ₀I/(2πr), proportional to I/r. Halving r DOUBLES B: not inverse square

Its direction

circles the wire. Grip with the right hand, thumb along the conventional current, fingers curl the way B runs. Never radial, never along the wire

Two parallel wires

same direction ATTRACT, opposite directions REPEL. Backwards from charges

Force on a wire

F = BIL sinθ, with L only the length INSIDE the field and θ between the current and B

Permeability

μ₀ = 4π × 10⁻⁷ T·m/A. B is measured in teslas

Flux

Φ = BA cosθ, with θ measured from the NORMAL to the loop, not from its plane

Edge-on loop

plane parallel to B puts the normal at 90°, so Φ = 0

Faraday's law

ε = −N ΔΦ/Δt. A RATE of change: a huge steady flux induces nothing

Reading a flux graph

the emf is the SLOPE, not the height. At the flux maximum the graph is flat, so the emf is zero

Three ways to induce

change B, change A, or change θ. A steady field with changing geometry still induces

Sliding bar on rails

ε = BLv, from the enclosed area growing at rate Lv

Rotating coil

θ changes continuously, which is how a generator works

Lenz's law

the induced current opposes the CHANGE in flux: it resists an increase and props up a decrease

Its mechanical check

the force on the induced current always resists the motion that produced it

Turns

an N-turn coil links the flux N times. Multiply BEFORE quoting any emf

Unit 12 tools

Challenge bank

1 / 60

60 open-ended problems.

Read the question, work it out, then flip the card to compare your reasoning to the worked solution. Mark each card so you can return to the ones that still bite.

Question

Tap card to reveal explanation

Worked solution

Tap card to return to question

Cumulative assessment

Test the unit.

Twenty mixed items drawn from across all 4 topics, with guaranteed misconception-code coverage. Identifies which misconceptions still bite when you cannot see which topic the question came from.

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Check what stuck.

Units 9 through 12, drawn evenly so earlier units get the same share as this one. Twenty questions or a full 42-question section, your choice. Even coverage means this is a retention check rather than a score estimate.

20 or 42questions

25topics

92codes covered

Begin assessment →