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 = 5 × 10⁵ m/sB = 0.2 T

An electron moves at 5 × 10⁵ m/s at an angle of 60° to a uniform magnetic field of 0.2 T. Find the magnitude of the magnetic force F on it.

|q| = 1.602 × 10⁻¹⁹ Cv = 5 × 10⁵ m/sB = 0.2 Tθ = 60°
F = fN
2.Easy
nB30°10 cm × 15 cmB = 0.4 T

A rectangular loop of 10 cm by 15 cm lies in a uniform magnetic field of 0.4 T. The field lines make an angle of 60° with the plane of the loop. Find the magnetic flux Φ through the loop.

B = 0.4 TA = 10 cm × 15 cm60° to the plane
Φ = mWb
3.Medium
nBA = 10 cm², N = 25B = 0.8 T

A coil of 25 turns has an area of 10 cm². The coil is turned over (rotated through 180°) in a uniform field of 0.8 T, which is perpendicular to its plane, in 250 ms. Find the average induced emf ε.

N = 25A = 10 cm²B = 0.8 TΔt = 250 ms
ε = mV
4.Medium
nBA = 80 cm², N = 500B: 0.2 → 1 T

A coil of 500 turns has an area of 80 cm². A uniform field perpendicular to the coil rises steadily from 0.2 T to 1 T in 500 ms. Find the average induced emf ε.

N = 500A = 80 cm²B: 0.2 T → 1 TΔt = 500 ms
ε = V
5.Hard
Bn = 900 rpm12 cm × 5 cmN = 250B = 0.5 T

A coil of 250 turns, 12 cm × 5 cm, rotates at 900 rpm in a uniform field of 0.5 T about an axis perpendicular to the field. Find the peak emf E0.

N = 250A = 12 cm × 5 cmB = 0.5 Tn = 900 rpm
E0 = V
6.Hard
E = 1 × 10⁴ V/m, B1​ = 0.4 TB2​ = 0.25 Tr = ?

A deuteron passes undeflected through a velocity selector with crossed fields E = 1 × 10⁴ V/m and B₁ = 0.4 T. It then enters a second region with only a magnetic field B₂ = 0.25 T, at right angles. Find the radius r of its path there.

E = 1 × 10⁴ V/mB1 = 0.4 TB2 = 0.25 Tm = 3.344 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ C
r = cm

Answer key

  1. 1. F = 13.87 fN
  2. 2. Φ = 5.196 mWb
  3. 3. ε = 160 mV
  4. 4. ε = 6.4 V
  5. 5. E0 = 70.69 V
  6. 6. r = 0.2087 cm

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