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
nB30°15 cm × 30 cmB = 0.1 T

A rectangular loop of 15 cm by 30 cm lies in a uniform magnetic field of 0.1 T. The field lines make an angle of 60° with the plane of the loop. Find the magnetic flux Φ through the loop.

B = 0.1 TA = 15 cm × 30 cm60° to the plane
Φ = mWb
2.Easy
nB60°12 cm × 15 cmB = 1.2 T

A rectangular loop of 12 cm by 15 cm lies in a uniform magnetic field of 1.2 T. The field makes an angle of 60° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 1.2 TA = 12 cm × 15 cm60° to the normal
Φ = mWb
3.Medium
nBA = 50 cm², N = 25B = 0.3 T

A coil of 25 turns has an area of 50 cm². The coil is turned over (rotated through 180°) in a uniform field of 0.3 T, which is perpendicular to its plane, in 100 ms. Find the average induced emf ε.

N = 25A = 50 cm²B = 0.3 TΔt = 100 ms
ε = mV
4.Medium
nBA = 20 cm², N = 20B: 0.05 → 0.35 T

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

N = 20A = 20 cm²B: 0.05 T → 0.35 TΔt = 20 msR = 20 Ω
I = mA
5.Hard
V = 2500 VB = 0.1 Tr = ?

An alpha particle starts from rest, is accelerated through a potential difference of 2500 V and then enters a uniform magnetic field of 0.1 T at right angles. Find the radius r of its path in the field.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ CV = 2500 VB = 0.1 T
r = cm
6.Hard
Bn = 600 rpm5 cm × 10 cmN = 150B = 0.2 T

A coil of 150 turns, 5 cm × 10 cm, rotates at 600 rpm in a uniform field of 0.2 T about an axis perpendicular to the field. Find the peak emf E0.

N = 150A = 5 cm × 10 cmB = 0.2 Tn = 600 rpm
E0 = V

Answer key

  1. 1. Φ = 3.897 mWb
  2. 2. Φ = 10.8 mWb
  3. 3. ε = 750 mV
  4. 4. I = 30 mA
  5. 5. r = 10.18 cm
  6. 6. E0 = 9.425 V

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