Electricity and Magnetism
What Electricity and Magnetism tests
This domain covers electrostatic force and field, electric potential, DC circuits, magnetic forces and fields, and electromagnetic induction. Expect quantitative problems that mix circuit analysis with energy or with a charged-particle trajectory.
Core rules
- Coulomb’s law: F = k|q1q2|/r^2. Electric field E = F/q, and for a point charge E = k|q|/r^2. Potential is scalar: V = kq/r.
- Ohm’s law V = IR. Resistors in series add; parallel conductances add. Kirchhoff’s junction and loop rules follow from charge and energy conservation.
- Magnetic force on a moving charge: F = qv × B, magnitude qvB sinθ. It does no work because it is perpendicular to velocity.
- Faraday’s law: emf = −dΦB/dt. Lenz’s law says the induced current opposes the change in flux, not necessarily the original field.
Worked example
A proton enters a 0.50 T field perpendicular to its velocity of 2.0 × 10^6 m/s. Find the radius of its circular path.
The magnetic force supplies centripetal force: qvB = mv^2/r, so r = mv/(qB). Using mp = 1.67 × 10^−27 kg and q = 1.60 × 10^−19 C: r = (1.67 × 10^−27)(2.0 × 10^6)/[(1.60 × 10^−19)(0.50)] = 4.2 × 10^−2 m. The path radius is about 4.2 cm. The speed remains constant because the force is centripetal.
Traps
Confusing electric field with potential; assuming a charged particle’s speed changes in a magnetic field; adding parallel resistors directly; ignoring battery internal resistance when asked; applying Lenz’s law to the field rather than to the flux change.