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
nB45°15 cm × 10 cmB = 0.6 T

A rectangular loop of 15 cm by 10 cm lies in a uniform magnetic field of 0.6 T. The field makes an angle of 45° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.6 TA = 15 cm × 10 cm45° to the normal
Φ = mWb
2.Easy
I = 10 APr = ?B = 200 µT

A long straight wire carries 10 A. At what distance r from the wire is the magnetic flux density 200 µT?

I = 10 AB = 200 µTμ₀ = 4π × 10⁻⁷ T·m/A
r = cm
3.Medium
IBF = ?

A wire carries a current to the right through a uniform magnetic field pointing into the page. Click the direction of the magnetic force on the wire.

I: to the rightB: into the page
  1. 1up the page
  2. 2to the right
  3. 3down the page
  4. 4to the left
4.Medium
nBA = 20 cm², N = 25B: 0.1 → 0.9 T

A coil of 25 turns, area 20 cm² and resistance 25 Ω forms a closed circuit. A uniform field perpendicular to the coil rises steadily from 0.1 T to 0.9 T in 100 ms. Find the average induced current I.

N = 25A = 20 cm²B: 0.1 T → 0.9 TΔt = 100 msR = 25 Ω
I = mA
5.Hard
N1​ = 2000, l = 20 cm50 A/sN2​ = 20Mε = ?

A short coil of 20 turns is wound tightly round the middle of a long solenoid of 2000 turns, length 20 cm and diameter 2 cm. The current in the solenoid changes at 50 A/s. Find the emf ε induced in the short coil.

N1 = 2000N2 = 20l = 20 cm⌀ = 2 cmdi/dt = 50 A/sμ₀ = 4π × 10⁻⁷ T·m/A
ε = mV
6.Hard
E = 2 × 10⁵ V/m, B1​ = 0.2 T

In a velocity selector, crossed fields E = 2 × 10⁵ V/m and B = 0.2 T let only ions of one speed pass straight through. Find that speed v.

E = 2 × 10⁵ V/mB1 = 0.2 T
v = m/s

Answer key

  1. 1. Φ = 6.364 mWb
  2. 2. r = 1 cm
  3. 3. up the page
  4. 4. I = 16 mA
  5. 5. ε = 3.948 mV
  6. 6. v = 1 × 10⁶ m/s

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