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
B0.5 T15 A45°L = 40 cm

A straight wire 40 cm long carries 15 A at an angle of 45° to a uniform magnetic field of 0.5 T. Find the magnitude of the force F on the wire.

B = 0.5 TI = 15 AL = 40 cmθ = 45°
F = N
2.Easy
B = ?I = 5 AL = 50 cmN = 1200

A solenoid 50 cm long has 1200 turns and carries 5 A. Find the magnetic flux density B inside it, far from the ends.

N = 1200L = 50 cmI = 5 Aμ₀ = 4π × 10⁻⁷ T·m/A
B = mT
3.Medium
nBA = 50 cm², N = 20B = 0.8 T

A coil of 20 turns has an area of 50 cm². The coil sits in a uniform field of 0.8 T perpendicular to its plane, and the field is switched off in 20 ms. Find the average induced emf ε.

N = 20A = 50 cm²B = 0.8 TΔt = 20 ms
ε = V
4.Medium
nBA = 40 cm², N = 250B = 0.2 T

A coil of 250 turns has an area of 40 cm². The coil is turned over (rotated through 180°) in a uniform field of 0.2 T, which is perpendicular to its plane, in 20 ms. Find the average induced emf ε.

N = 250A = 40 cm²B = 0.2 TΔt = 20 ms
ε = V
5.Hard
I = 1 Al = 40 cmN = 800, ⌀ 2.5 cm

A long air-core solenoid has 800 turns, a length of 40 cm and a diameter of 2.5 cm. Find the energy W stored in its magnetic field when it carries 1 A.

N = 800l = 40 cm⌀ = 2.5 cmI = 1 Aμ₀ = 4π × 10⁻⁷ T·m/A
W = µJ
6.Hard
E = 5 × 10⁴ V/m, B1​ = 0.2 TB2​ = 0.25 Tr = ?

A deuteron passes undeflected through a velocity selector with crossed fields E = 5 × 10⁴ V/m and B₁ = 0.2 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 = 5 × 10⁴ V/mB1 = 0.2 TB2 = 0.25 Tm = 3.344 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ C
r = cm

Answer key

  1. 1. F = 2.121 N
  2. 2. B = 15.08 mT
  3. 3. ε = 4 V
  4. 4. ε = 20 V
  5. 5. W = 493.5 µJ
  6. 6. r = 2.087 cm

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