Magnetic Effects of Current and Magnetism
This domain tests moving charges and currents as sources of magnetic field, forces on charges and wires, torque on loops, moving-coil galvanometers, and magnetic properties of materials. The exam expects vector directions from the right-hand rule and correct use of sine and cosine factors.
Core rules and concepts
- A charge q moving with velocity v in field B feels F = qv x B; magnitude qvB sin(theta). A wire carrying current I in field B feels F = IL x B.
- Magnetic force does no work on a charged particle; it changes direction, not speed.
- Biot-Savart law gives field contributions from current elements. For a long straight wire B = mu0 I/(2 pi r). At the centre of a circular loop B = mu0 I/(2R). Inside a long solenoid B = mu0 n I.
- Ampere law is useful with high symmetry.
- A current loop has magnetic dipole moment m = NIA; torque tau = m x B, magnitude NIAB sin(theta).
- A moving-coil galvanometer uses a radial field so torque is proportional to current; sensitivity depends on N, A, B, and torsional constant.
- Dia-, para-, and ferromagnetic materials differ in permeability and temperature behaviour.
Worked example
A proton with speed 2.0 x 10^6 m/s enters perpendicular to B = 0.50 T. Force magnitude is qvB = (1.6e-19)(2.0e6)(0.50) = 1.6e-13 N. The radius of the circular path is r = mv/(qB) = (1.67e-27 x 2.0e6)/(1.6e-19 x 0.50), which is about 0.042 m, or 4.2 cm.
Traps that cost marks
- Using the right-hand rule without reversing direction for a negative charge.
- Forgetting sin(theta) when velocity or wire is not perpendicular to B.
- Claiming magnetic force changes kinetic energy.
- Mixing up field at the centre of a loop and on the axis.
- Ignoring that a galvanometer needs a radial field for a linear scale.