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 = 3 × 10⁵ m/sB = 0.5 T

A proton moves at 3 × 10⁵ m/s at an angle of 30° to a uniform magnetic field of 0.5 T. Find the magnitude of the magnetic force F on it.

|q| = 1.602 × 10⁻¹⁹ Cv = 3 × 10⁵ m/sB = 0.5 Tθ = 30°
F = fN
2.Easy
I = 1.5 AR = 3 cmB = ?N = 5

A flat circular coil of 5 turns and radius 3 cm carries a current of 1.5 A. Find the magnetic flux density B at its centre.

N = 5I = 1.5 AR = 3 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
3.Medium
nBA = 50 cm², N = 100B = 0.2 T

A coil of 100 turns has an area of 50 cm². The coil is turned over (rotated through 180°) in a uniform field of 0.2 T, which is perpendicular to its plane, in 500 ms. Find the average induced emf ε.

N = 100A = 50 cm²B = 0.2 TΔt = 500 ms
ε = mV
4.Medium
nBA = 200 cm², N = 100B: 0.2 → 1 T

A coil of 100 turns, area 200 cm² and resistance 20 Ω forms a closed circuit. A uniform field perpendicular to the coil rises steadily from 0.2 T to 1 T in 40 ms. Find the average induced current I.

N = 100A = 200 cm²B: 0.2 T → 1 TΔt = 40 msR = 20 Ω
I = A
5.Hard
I = 2.5 Al = 40 cmN = 1000, ⌀ 1 cm

A long air-core solenoid has 1000 turns, a length of 40 cm and a diameter of 1 cm. Find the energy W stored in its magnetic field when it carries 2.5 A.

N = 1000l = 40 cm⌀ = 1 cmI = 2.5 Aμ₀ = 4π × 10⁻⁷ T·m/A
W = µJ
6.Hard
V = 2500 VB = 0.25 Tr = ?

A proton starts from rest, is accelerated through a potential difference of 2500 V and then enters a uniform magnetic field of 0.25 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 = 2500 VB = 0.25 T
r = cm

Answer key

  1. 1. F = 12.01 fN
  2. 2. B = 157.1 µT
  3. 3. ε = 400 mV
  4. 4. I = 2 A
  5. 5. W = 771.1 µJ
  6. 6. r = 2.89 cm

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