Magnetic fields & induction worksheet with answers

Free printable Magnetic fields & induction worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
nB20°12 cm × 30 cmB = 0.2 T

A rectangular loop of 12 cm by 30 cm lies in a uniform magnetic field of 0.2 T. The field makes an angle of 20° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.2 TA = 12 cm × 30 cm20° to the normal
Φ = mWb
2.Easy
B0.08 T20 A90°L = 100 cm

A straight wire 100 cm long carries 20 A at an angle of 90° to a uniform magnetic field of 0.08 T. Find the magnitude of the force F on the wire.

B = 0.08 TI = 20 AL = 100 cmθ = 90°
F = N
3.Medium
R = 4 Ωv = 2.5 m/sL = 80 cmB = 1 T

A metal rod 80 cm long slides at 2.5 m/s along two rails in a uniform field of 1 T into the page. The rails are joined by a resistor of 4 Ω; the rod and rails have negligible resistance. Find the power P dissipated in the resistor.

B = 1 TL = 80 cmv = 2.5 m/sR = 4 Ω
P = W
4.Medium
nBA = 150 cm², N = 20B: 0.05 → 0.35 T

A coil of 20 turns, area 150 cm² and resistance 5 Ω forms a closed circuit. A uniform field perpendicular to the coil rises steadily from 0.05 T to 0.35 T in 500 ms. Find the average induced current I.

N = 20A = 150 cm²B: 0.05 T → 0.35 TΔt = 500 msR = 5 Ω
I = mA
5.Hard
N1​ = 1000, l = 25 cm100 A/sN2​ = 100Mε = ?

A short coil of 100 turns is wound tightly round the middle of a long solenoid of 1000 turns, length 25 cm and diameter 3 cm. The current in the solenoid changes at 100 A/s. Find the emf ε induced in the short coil.

N1 = 1000N2 = 100l = 25 cm⌀ = 3 cmdi/dt = 100 A/sμ₀ = 4π × 10⁻⁷ T·m/A
ε = mV
6.Hard
I = 1.5 Al = 20 cmN = 1000, ⌀ 2.5 cm

A long air-core solenoid has 1000 turns, a length of 20 cm and a diameter of 2.5 cm. Find the energy W stored in its magnetic field when it carries 1.5 A.

N = 1000l = 20 cm⌀ = 2.5 cmI = 1.5 Aμ₀ = 4π × 10⁻⁷ T·m/A
W = mJ

Answer key

  1. 1. Φ = 6.766 mWb
  2. 2. F = 1.6 N
  3. 3. P = 1 W
  4. 4. I = 36 mA
  5. 5. ε = 35.53 mV
  6. 6. W = 3.47 mJ

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