Magnetic Effects of Current and Magnetism
Here the exam tests how currents create magnetic fields (Biot–Savart law, straight wire, circular loop, solenoid) and how those fields act on moving charges and current-carrying conductors. Expect one derivation-type long answer - field at the centre of a circular loop or force per unit length between parallel wires - and short numericals on radius of a circular path, torque on a coil, or conversion of a galvanometer into an ammeter or voltmeter.
Core rules
- Straight wire: B = μ₀I/2πr. Circular loop at its centre: B = μ₀I/2R; for N turns multiply by N. Long solenoid: B = μ₀nI.
- Force on a moving charge: F = qvB sinθ, always perpendicular to both v and B, so it does no work and the speed stays constant.
- Circular path in a uniform field: r = mv/qB; time period T = 2πm/qB is independent of speed - the basis of the cyclotron.
- Force on a wire: F = BIL sinθ; torque on a coil: τ = NIAB sinθ.
- Moving-coil galvanometer: deflection proportional to current. Shunt for ammeter: S = I(g)G/(I − I(g)). Series resistance for voltmeter: R = V/I(g) − G.
Worked example
A long straight wire carries 5 A. Find the magnetic field at 10 cm from it. B = μ₀I/2πr = (4π×10⁻⁷ × 5)/(2π × 0.10) = (2×10⁻⁷ × 5)/0.10 = 1×10⁻⁵ T. Reasoning check: the field is 2×10⁻⁷ × I/r with r in metres, so doubling the distance to 20 cm would halve the field to 5×10⁻⁶ T.
Traps that cost marks
- Using degrees instead of radians or forgetting to convert cm to m in the Biot–Savart formulas.
- Claiming the magnetic force changes the kinetic energy of a charged particle; it cannot, because F ⊥ v.
- Reversing the right-hand rule direction for a current loop or solenoid.
- Mixing the shunt (parallel, low resistance) and series-multiplier (series, high resistance) formulas.