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 solenoid 15 cm long carries 1.5 A. How many turns N must it have for a flux density of 15.08 mT inside?

I = 1.5 AL = 15 cmB = 15.08 mTμ₀ = 4π × 10⁻⁷ T·m/A

N =

2.Easy

A rectangular loop of 5 cm by 10 cm lies in a uniform magnetic field of 0.2 T. The field makes an angle of 37° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.2 TA = 5 cm × 10 cm37° to the normal

Φ = mWb

3.Medium

A coil of 10 turns has an area of 80 cm². A uniform field perpendicular to the coil rises steadily from 0.2 T to 0.8 T in 40 ms. Find the average induced emf ε.

N = 10A = 80 cm²B: 0.2 T → 0.8 TΔt = 40 ms

ε = V

4.Medium

Two long parallel wires 5 cm apart carry currents of 5 A and 15 A in opposite directions. Find the force per metre of length F/L between them.

I₁ = 5 AI₂ = 15 Ad = 5 cmμ₀ = 4π × 10⁻⁷ T·m/A

F/L = µN/m

5.Hard

A proton starts from rest, is accelerated through a potential difference of 5000 V and then enters a uniform magnetic field of 0.3 T at right angles. Find the radius r of its path in the field.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CV = 5000 VB = 0.3 T

r = cm

6.Hard

A long air-core solenoid has 300 turns, a length of 40 cm and a diameter of 4 cm. Find the energy W stored in its magnetic field when it carries 1 A.

N = 300l = 40 cm⌀ = 4 cmI = 1 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = µJ

Answer key

1. N = 1200
2. Φ = 0.7986 mWb
3. ε = 1.2 V
4. F/L = 300 µN/m
5. r = 3.406 cm
6. W = 177.7 µJ

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