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 = 3 AL = 40 cmN = 1500

A solenoid 40 cm long has 1500 turns and carries 3 A. Find the magnetic flux density B inside it, far from the ends.

N = 1500L = 40 cmI = 3 Aμ₀ = 4π × 10⁻⁷ T·m/A
B = mT
2.Easy
B = 10.05 mTI = 4 AL = 20 cmN = ?

A solenoid 20 cm long carries 4 A. How many turns N must it have for a flux density of 10.05 mT inside?

I = 4 AL = 20 cmB = 10.05 mTμ₀ = 4π × 10⁻⁷ T·m/A
N =
3.Medium
nBA = 40 cm², N = 50B = 0.3 T

A coil of 50 turns has an area of 40 cm². The coil sits in a uniform field of 0.3 T perpendicular to its plane, and the field is switched off in 100 ms. Find the average induced emf ε.

N = 50A = 40 cm²B = 0.3 TΔt = 100 ms
ε = mV
4.Medium
nBA = 200 cm², N = 20B: 0.1 → 0.5 T

A coil of 20 turns has an area of 200 cm². A uniform field perpendicular to the coil rises steadily from 0.1 T to 0.5 T in 200 ms. Find the average induced emf ε.

N = 20A = 200 cm²B: 0.1 T → 0.5 TΔt = 200 ms
ε = mV
5.Hard
l = 15 cmN = 500, ⌀ 2 cm

A long air-core solenoid has 500 turns, a length of 15 cm and a diameter of 2 cm. Find its self-inductance L.

N = 500l = 15 cm⌀ = 2 cmμ₀ = 4π × 10⁻⁷ T·m/A
L = µH
6.Hard
E = 1 × 10⁴ V/m, B1​ = 0.1 T

In a velocity selector, crossed fields E = 1 × 10⁴ V/m and B = 0.1 T let only ions of one speed pass straight through. Find that speed v.

E = 1 × 10⁴ V/mB1 = 0.1 T
v = m/s

Answer key

  1. 1. B = 14.14 mT
  2. 2. N = 399.9
  3. 3. ε = 600 mV
  4. 4. ε = 800 mV
  5. 5. L = 658 µH
  6. 6. v = 100000 m/s

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