ap physics c - magnetism - april 2026

mass spectrometer (slow ions)

m=rqBB’/E

mass spectrometer (fast ions)

m=r²qB²/2V

radius of circular motion

r=mvsinθ/qB

potential energy with given voltage

qV

magnetic force on a moving charge

F=qv x B

what happens to the charge when the angle between v & B is 90° vs. other angle?

90°, moves in a circle

other angle, moves in a helix

period of rotation

T = 2πm/qB = 2π/w

angular frequency

w=qB/m

pitch (distance travelled up in 1 T)

P=2πmvcosθ/qB

Hall Effect

Voltage generated across wire in circuit in a B

V = ILB/nAe

Force on a current-carrying wire in a magnetic field

F=ILBsinθ

Torque on a loop of wire

τ=NIABsinθ

Biôt-Savart Law

B=∫(μ/4π)IdL/(4πr²)

in the radial direction

for simple shapes

μ

μ = 4π x 10^-7

BSL: Infinitely long straight wire

μI/2πR

BSL: Arc of current

μIθ/4πR

BSL: Complete loop of wire

B=μI/2R

Forces between current-carrying wires

F=I₁I₂μL/2πR

Parallel = attract, opposites = repel

Ampere’s Law

∫Bds=μI_encl

B inside current-carrying wire

J constant

B=μIr/2πR²

J=f(r)

∫Bds=μ∫f(r)2πrdr

B inside solenoid

B = NμI/L

B inside and outside torroid

B = NμI/2πr

B_outside = 0

Ferromagnetism

The B of one electron could influence another, external B makes electrons line up and when it is removed, they stay lined up

Paramagnetism

When you remove the B, the electrons go back to their random states

Dimagnetism

Most electrons do not line up with an external B