Electromagnetism

NUST NET (Engineering) · Physics · Magnetism and alternating current. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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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

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?

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

Answer: 0.080 m (8.0 cm)

Practice questions

Try each one, then open the answer.

1. A rectangular coil of 50 turns and area 0.020 m2 carries 2.0 A in a uniform field of 0.50 T, with the plane of the coil parallel to the field. The torque on the coil is

  1. A
    zero
  2. B
    0.020 N m
  3. C
    1.0 N m
  4. D
    2.0 N m
Show answer

Answer: C. τ = NBIA cos α, where α is the angle between the plane of the coil and the field. Here α = 0°, so τ = 50 × 0.50 × 2.0 × 0.020 = 1.0 N m, the largest value. The torque is zero when the plane is perpendicular to the field.

2. The tesla, the SI unit of magnetic flux density, is equal to

  1. A
    N A m
  2. B
    N A−1 m−1
  3. C
    N A−1 m
  4. D
    Wb m2
Show answer

Answer: B. From F = BIL, B = F/(IL), so 1 T = 1 N ÷ (1 A × 1 m) = 1 N A−1 m−1. It is also 1 Wb m−2 (flux per unit area), not Wb m2.

3. A galvanometer of resistance 50 Ω gives full-scale deflection at 1.0 mA. To convert it into an ammeter of range 0–1.0 A, you should connect

  1. A
    about 0.05 Ω in series
  2. B
    950 Ω in series
  3. C
    about 0.05 Ω in parallel
  4. D
    50 Ω in parallel
Show answer

Answer: C. A shunt goes in parallel and carries the extra 0.999 A: Rs = IgRg/(I − Ig) = (0.001 × 50)/0.999 ≈ 0.05 Ω. A series resistance is what turns a galvanometer into a voltmeter.

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