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
nB53°12 cm × 15 cmB = 0.8 T

A rectangular loop of 12 cm by 15 cm lies in a uniform magnetic field of 0.8 T. The field makes an angle of 53° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.8 TA = 12 cm × 15 cm53° to the normal
Φ = mWb
2.Easy
−v = 1.5 × 10⁵ m/sB = 1.5 T

An electron moves at 1.5 × 10⁵ m/s perpendicular to a uniform magnetic field of 1.5 T. Find the magnitude of the magnetic force F on it.

|q| = 1.602 × 10⁻¹⁹ Cv = 1.5 × 10⁵ m/sB = 1.5 Tθ = 90°
F = fN
3.Medium
nBA = 20 cm², N = 25B = 0.5 T

A coil of 25 turns has an area of 20 cm². The coil is turned over (rotated through 180°) in a uniform field of 0.5 T, which is perpendicular to its plane, in 200 ms. Find the average induced emf ε.

N = 25A = 20 cm²B = 0.5 TΔt = 200 ms
ε = mV
4.Medium
10 A8 Ad = 4 cm

Two long parallel wires 4 cm apart carry currents of 10 A and 8 A in opposite directions. Find the force per metre of length F/L between them.

I1 = 10 AI2 = 8 Ad = 4 cmμ₀ = 4π × 10⁻⁷ T·m/A
F/L = µN/m
5.Hard
Bn = ?20 cm × 5 cmN = 250B = 0.1 T

A coil of 250 turns, 20 cm × 5 cm, rotates in a uniform field of 0.1 T about an axis perpendicular to the field. At what speed n (in revolutions per minute) must it turn to give an rms emf of 11.11 V?

N = 250A = 20 cm × 5 cmB = 0.1 TErms = 11.11 V
n = rpm
6.Hard
E = 1 × 10⁵ V/m, B1​ = 0.25 TB2​ = 0.5 Tr = ?

A proton passes undeflected through a velocity selector with crossed fields E = 1 × 10⁵ V/m and B₁ = 0.25 T. It then enters a second region with only a magnetic field B₂ = 0.5 T, at right angles. Find the radius r of its path there.

E = 1 × 10⁵ V/mB1 = 0.25 TB2 = 0.5 Tm = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ C
r = cm

Answer key

  1. 1. Φ = 8.666 mWb
  2. 2. F = 36.04 fN
  3. 3. ε = 250 mV
  4. 4. F/L = 400 µN/m
  5. 5. n = 600.2 rpm
  6. 6. r = 0.8355 cm

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