AP Physics 2 · AP Physics 2 CED: Magnetic Fields and Forces · 16 min read
1. Magnetic Force on Charges and Currents★★☆☆☆⏱ 4 min
Magnetic fields exert force only on **moving** charges. Stationary charges experience zero magnetic force, a key point frequently tested on the AP Physics 2 exam.
F_B = qvB\sin\theta
$q$ = magnitude of the moving charge (C)
$v$ = speed of the charge (m/s)
$B$ = magnetic field magnitude (tesla, T)
$\theta$ = angle between velocity and magnetic field vectors
Direction of the force is found with the right-hand rule (RHR) for positive charges: point right hand fingers along velocity, curl toward the magnetic field direction, thumb points to force direction. For negative charges, reverse the force direction.
F_B = ILB\sin\theta
Where $I$ is current (A), $L$ is length of the wire inside the field, and $\theta$ is the angle between current direction and the magnetic field.
2. Magnetic Fields of Long Wires and Solenoids★★☆☆☆⏱ 4 min
Moving charges (electric currents) produce magnetic fields around them. Two common configurations tested on AP Physics 2 are infinitely long straight wires and solenoids (tightly wound coils of wire).
B = \frac{\mu_0 I}{2\pi r}
Where $\mu_0 = 4\pi \times 10^{-7}$ T·m/A, the permeability of free space (provided on the AP Physics 2 equation sheet). Direction is given by the right-hand grip rule: grip the wire with your right hand, thumb along current, curled fingers follow magnetic field lines (which form concentric circles around the wire).
B = \mu_0 n I
Where $n = \frac{N}{L}$, the number of turns $N$ per unit length $L$ of the solenoid. Direction is found by right-hand grip for coils: curl fingers along current direction, thumb points to the north pole and direction of internal magnetic field.
3. Faraday's Law and Lenz's Law★★★☆☆⏱ 4 min
Electromagnetic induction occurs when a changing magnetic flux through a closed conducting loop induces an electromotive force (EMF), which drives an induced current if the loop is closed.
\Phi_B = BA\cos\theta
Where $A$ is the area of the loop, and $\theta$ is the angle between the magnetic field vector and the normal vector (a line perpendicular to the plane of the loop). The unit of flux is the weber (1 Wb = 1 T·m²).
\varepsilon = -N \frac{\Delta \Phi_B}{\Delta t}
The negative sign is explained by Lenz's Law, which gives the direction of the induced current:
4. Induced EMF in Moving Conducting Rods★★★☆☆⏱ 4 min
Motional EMF is a special case of Faraday's Law where a conducting rod moving through a magnetic field develops a potential difference across its ends, even if it is not part of a closed circuit.
Common Pitfalls
Why: Students memorize the RHR for positive charges and forget that negative charge reverses the force direction
Why: Misinterpretation of the $\theta$ definition in the flux formula
Why: Mixing up the formulas for long wires and solenoids
Why: Oversimplification of the 'oppose' rule in Lenz's law
Why: Forgetting that $\sin0^\circ = 0$, so force/EMF is zero