Magnetic Effects of Current and Magnetism
What the exam tests
Questions cover Biot-Savart law, magnetic field due to straight wires, loops and solenoids, force on moving charges and current-carrying conductors, torque on loops, moving-coil galvanometer and conversion to ammeter or voltmeter.
Core rules
- Long straight wire: B = μ0I/(2πr). Centre of a circular loop: B = μ0I/(2R). Solenoid: B = μ0nI.
- Force on a charge: F = qvB sinθ; direction by right-hand rule. For v perpendicular to B, radius r = mv/(qB) and period T = 2πm/(qB), independent of speed.
- Force on a wire: F = BIL sinθ. Parallel wires carrying currents in the same direction attract each other.
- Torque on a coil: τ = NIAB sinθ, where θ is the angle between the normal to the coil and B. Magnetic moment m = NIA.
- Moving-coil galvanometer deflection is proportional to current. A shunt gives an ammeter; a high series resistance gives a voltmeter.
Worked example
Two long parallel wires 0.20 m apart carry 4 A and 6 A in the same direction. Find the force per unit length. Use F/L = μ0I1I2/(2πd) = (2×10^-7)(4)(6)/(0.20) = 2.4×10^-5 N/m. The force is attractive because the currents are parallel. If the currents were opposite, the force would be repulsive.
Traps
Use the angle between v and B for a moving charge, but the angle between the coil normal and B for torque. The force is zero when the charge moves parallel to B, even if B is strong. Right-hand rule errors are common. Torque is maximum when the plane of the coil is parallel to B, not when the normal is parallel. A shunt is low resistance, not high.