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
B = ?I = 1.5 AL = 25 cmN = 2000

A solenoid 25 cm long has 2000 turns and carries 1.5 A. Find the magnetic flux density B inside it, far from the ends.

N = 2000L = 25 cmI = 1.5 Aμ₀ = 4π × 10⁻⁷ T·m/A
B = mT
2.Easy
B0.8 TI = ?30°L = 20 cm

A straight wire 20 cm long lies at 30° to a uniform magnetic field of 0.8 T. The magnetic force on it is 0.8 N. Find the current I.

B = 0.8 TF = 0.8 NL = 20 cmθ = 30°
I = A
3.Medium
12 A8 Ad = 4 cmP

Two long parallel wires 4 cm apart carry currents of 12 A and 8 A in the same direction. Find the magnitude of the magnetic flux density B at point P, halfway between them.

I1 = 12 AI2 = 8 Ad = 4 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
4.Medium
nBA = 20 cm², N = 200B: 0.2 → 0.4 T

A coil of 200 turns has an area of 20 cm². A uniform field perpendicular to the coil rises steadily from 0.2 T to 0.4 T in 100 ms. Find the average induced emf ε.

N = 200A = 20 cm²B: 0.2 T → 0.4 TΔt = 100 ms
ε = mV
5.Hard
l = 40 cmN = 2000, ⌀ 2.5 cm

A long air-core solenoid has 2000 turns, a length of 40 cm and a diameter of 2.5 cm. Find its self-inductance L.

N = 2000l = 40 cm⌀ = 2.5 cmμ₀ = 4π × 10⁻⁷ T·m/A
L = mH
6.Hard
E = 2 × 10⁵ V/m, B1​ = 0.5 T

In a velocity selector, crossed fields E = 2 × 10⁵ V/m and B = 0.5 T let only ions of one speed pass straight through. Find that speed v.

E = 2 × 10⁵ V/mB1 = 0.5 T
v = m/s

Answer key

  1. 1. B = 15.08 mT
  2. 2. I = 10 A
  3. 3. B = 40 µT
  4. 4. ε = 800 mV
  5. 5. L = 6.169 mH
  6. 6. v = 400000 m/s

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