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
I = 4 AR = 10 cmB = ?N = 10

A flat circular coil of 10 turns and radius 10 cm carries a current of 4 A. Find the magnetic flux density B at its centre.

N = 10I = 4 AR = 10 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
2.Easy
B = ?I = 2.5 AL = 30 cmN = 200

A solenoid 30 cm long has 200 turns and carries 2.5 A. Find the magnetic flux density B inside it, far from the ends.

N = 200L = 30 cmI = 2.5 Aμ₀ = 4π × 10⁻⁷ T·m/A
B = mT
3.Medium
R = 4 Ωv = 3 m/sL = 20 cmB = 0.2 T

A metal rod 20 cm long slides at 3 m/s along two rails in a uniform field of 0.2 T into the page. The rails are joined by a resistor of 4 Ω; the rod and rails have negligible resistance. Find the force F needed to keep the rod moving at constant speed (no friction).

B = 0.2 TL = 20 cmv = 3 m/sR = 4 Ω
F = mN
4.Medium
nBA = 200 cm², N = 10B = 0.8 T

A coil of 10 turns has an area of 200 cm². The coil sits in a uniform field of 0.8 T perpendicular to its plane, and the field is switched off in 500 ms. Find the average induced emf ε.

N = 10A = 200 cm²B = 0.8 TΔt = 500 ms
ε = mV
5.Hard
l = 10 cmN = 300, ⌀ 2.5 cm

A long air-core solenoid has 300 turns, a length of 10 cm and a diameter of 2.5 cm. Find its self-inductance L.

N = 300l = 10 cm⌀ = 2.5 cmμ₀ = 4π × 10⁻⁷ T·m/A
L = µH
6.Hard
E = 8 × 10⁴ V/m, B1​ = 0.2 TB2​ = 0.4 Tr = ?

A proton passes undeflected through a velocity selector with crossed fields E = 8 × 10⁴ V/m and B₁ = 0.2 T. It then enters a second region with only a magnetic field B₂ = 0.4 T, at right angles. Find the radius r of its path there.

E = 8 × 10⁴ V/mB1 = 0.2 TB2 = 0.4 Tm = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ C
r = cm

Answer key

  1. 1. B = 251.3 µT
  2. 2. B = 2.094 mT
  3. 3. F = 1.2 mN
  4. 4. ε = 320 mV
  5. 5. L = 555.2 µH
  6. 6. r = 1.044 cm

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