Magnetic Effects of Current and Magnetism
This domain covers magnetic fields of currents, forces on charges and conductors, moving-coil instruments and magnetic materials. PSEB questions often ask for magnitude and direction together, so use the right-hand rule explicitly.
Core rules and concepts
- Biot–Savart law gives dB = (μ0/4π)(I dl × r)/r³. For a long straight wire B = μ0I/2πr; at the centre of a circular loop B = μ0I/2R; inside a solenoid B = μ0nI.
- Force on a charge: F = qvB sinθ, perpendicular to v and B. Force on a conductor: F = ILB sinθ.
- A charge moving perpendicular to a uniform B follows a circle of radius r = mv/qB; cyclotron frequency is f = qB/2πm.
- A current loop has magnetic moment m = NIA; torque τ = mB sinθ. A moving-coil galvanometer deflection is proportional to current.
- Magnetic field lines are closed loops; like poles repel, unlike attract. Soft iron is easily magnetised; steel retains magnetism.
Worked example
A proton (m = 1.67×10⁻²⁷ kg, q = 1.6×10⁻¹⁹ C) moves at 2×10⁶ m s⁻¹ perpendicular to B = 0.5 T. Find the force and orbit radius. F = qvB = (1.6×10⁻¹⁹)(2×10⁶)(0.5) = 1.6×10⁻¹³ N. r = mv/qB = (1.67×10⁻²⁷)(2×10⁶)/[(1.6×10⁻¹⁹)(0.5)] = 4.2×10⁻² m, about 4.2 cm.
Traps
- Magnetic force is zero when v is parallel to B, even if the speed is large.
- Magnetic force does no work; it changes direction, not speed or kinetic energy.
- Use the right-hand rule for a positive charge; reverse the result for an electron.
- A current-carrying loop in a uniform field may have zero net force but nonzero torque.