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
+v = 6 × 10⁶ m/sB = 0.1 T

A proton moves at 6 × 10⁶ m/s at an angle of 45° to a uniform magnetic field of 0.1 T. Find the magnitude of the magnetic force F on it.

|q| = 1.602 × 10⁻¹⁹ Cv = 6 × 10⁶ m/sB = 0.1 Tθ = 45°
F = fN
2.Easy
+v = 1.5 × 10⁶ m/sB = 1.5 T

A proton moves at 1.5 × 10⁶ m/s at an angle of 45° 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 × 10⁶ m/sB = 1.5 Tθ = 45°
F = fN
3.Medium
R = 2.5 Ωv = 2 m/sL = 20 cmB = 0.25 T

A metal rod 20 cm long slides at 2 m/s along two rails in a uniform field of 0.25 T into the page. The rails are joined by a resistor of 2.5 Ω; the rod and rails have negligible resistance. Find the current I.

B = 0.25 TL = 20 cmv = 2 m/sR = 2.5 Ω
I = mA
4.Medium
nBA = 50 cm², N = 250B: 0.05 → 0.45 T

A coil of 250 turns, area 50 cm² and resistance 8 Ω forms a closed circuit. A uniform field perpendicular to the coil rises steadily from 0.05 T to 0.45 T in 20 ms. Find the average induced current I.

N = 250A = 50 cm²B: 0.05 T → 0.45 TΔt = 20 msR = 8 Ω
I = A
5.Hard
Bn = 3600 rpm10 cm × 5 cmN = 200B = 0.2 T

A coil of 200 turns, 10 cm × 5 cm, rotates at 3600 rpm in a uniform field of 0.2 T about an axis perpendicular to the field. Find the rms value Erms of the emf.

N = 200A = 10 cm × 5 cmB = 0.2 Tn = 3600 rpm
Erms = V
6.Hard
V = 1000 VB = 0.5 Tr = ?

A proton starts from rest, is accelerated through a potential difference of 1000 V and then enters a uniform magnetic field of 0.5 T at right angles. Find the radius r of its path in the field.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CV = 1000 VB = 0.5 T
r = cm

Answer key

  1. 1. F = 67.97 fN
  2. 2. F = 254.9 fN
  3. 3. I = 40 mA
  4. 4. I = 3.125 A
  5. 5. Erms = 53.31 V
  6. 6. r = 0.914 cm

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