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

A rectangular loop of 15 cm by 10 cm lies in a uniform magnetic field of 0.25 T. The field makes an angle of 0° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.25 TA = 15 cm × 10 cm0° to the normal

Φ = mWb

2.Easy

A straight wire 15 cm long lies at 45° to a uniform magnetic field of 0.3 T. The magnetic force on it is 0.06364 N. Find the current I.

B = 0.3 TF = 0.06364 NL = 15 cmθ = 45°

I = A

3.Medium

A coil of 50 turns has an area of 10 cm². A uniform field perpendicular to the coil rises steadily from 0.2 T to 0.6 T in 250 ms. Find the average induced emf ε.

N = 50A = 10 cm²B: 0.2 T → 0.6 TΔt = 250 ms

ε = mV

4.Medium

A coil of 250 turns has an area of 50 cm². A uniform field perpendicular to the coil rises steadily from 0.2 T to 0.5 T in 500 ms. Find the average induced emf ε.

N = 250A = 50 cm²B: 0.2 T → 0.5 TΔt = 500 ms

ε = mV

5.Hard

A short coil of 200 turns is wound tightly round the middle of a long solenoid of 800 turns, length 20 cm and diameter 4 cm. Find their mutual inductance M.

N₁ = 800N₂ = 200l = 20 cm⌀ = 4 cmμ₀ = 4π × 10⁻⁷ T·m/A

M = mH

6.Hard

An alpha particle starts from rest, is accelerated through a potential difference of 1000 V and then enters a uniform magnetic field of 0.8 T at right angles. Find the radius r of its path in the field.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ CV = 1000 VB = 0.8 T

r = cm

Answer key

1. Φ = 3.75 mWb
2. I = 2 A
3. ε = 80 mV
4. ε = 750 mV
5. M = 1.263 mH
6. r = 0.8051 cm

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