Electromagnetism

NUST NET Physics · Physics · Magnetism and alternating current. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A magnetic field pushes on moving charge, whether that charge is a current in a wire or a single particle. The force is greatest when the motion is at right angles to the field and zero when it is along the field. Its direction is perpendicular to both the field and the motion.

Because the force on a moving particle is always at right angles to its velocity, it changes the direction but not the speed. The particle moves in a circle and the field does no work on it.

A galvanometer detects small currents. A small shunt resistance in parallel turns it into an ammeter; a large resistance in series turns it into a voltmeter.

Rules to remember

Force on a wire = BIL sin θ, θ between the wire and the field; so 1 T = 1 N A⁻¹ m⁻¹
Force on a moving charge = qvB sin θ, θ between the velocity and the field
Charge moving at right angles to the field: radius r = mv/(qB); period T = 2πm/(qB), which does not depend on speed
Field inside a long solenoid: B = μ₀nI, where n = turns per metre and μ₀ = 4π × 10⁻⁷ T m A⁻¹
Torque on a coil = NIAB cos α, α between the plane of the coil and the field (maximum NIAB when the plane is parallel to the field)
Ammeter: shunt in parallel, R_s = I_gR_g/(I − I_g)
Voltmeter: high resistance in series, R_h = (V/I_g) − R_g

Common mistake

Swapping the two conversions. An ammeter needs a very low resistance, so the shunt goes in parallel; a voltmeter needs a very high resistance, so the extra resistor goes in series.

Worked example

A particle of mass 6.4 × 10⁻²⁷ kg and charge 3.2 × 10⁻¹⁹ C moves at 2.0 × 10⁶ m s⁻¹ at right angles to a uniform field of 0.50 T. What is the radius of its path?

The magnetic force supplies the centripetal force: qvB = mv²/r, so r = mv/(qB).
mv = 6.4 × 10⁻²⁷ × 2.0 × 10⁶ = 1.28 × 10⁻²⁰ kg m s⁻¹.
qB = 3.2 × 10⁻¹⁹ × 0.50 = 1.6 × 10⁻¹⁹.
r = (1.28 × 10⁻²⁰)/(1.6 × 10⁻¹⁹) = 0.080 m.

Answer: 0.080 m (8.0 cm)

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