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 single circular loop of wire with radius 15 cm carries a current of 3 A. Find the magnetic flux density B at its centre.

N = 1I = 3 AR = 15 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

2.Easy

A rectangular loop of 5 cm by 30 cm lies in a uniform magnetic field of 0.8 T. The field makes an angle of 30° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.8 TA = 5 cm × 30 cm30° to the normal

Φ = mWb

3.Medium

A coil of 25 turns has an area of 40 cm². The coil is turned over (rotated through 180°) in a uniform field of 0.3 T, which is perpendicular to its plane, in 10 ms. Find the average induced emf ε.

N = 25A = 40 cm²B = 0.3 TΔt = 10 ms

ε = V

4.Medium

Two long parallel wires 20 cm apart carry currents of 10 A and 25 A in the same direction. Find the force per metre of length F/L between them.

I₁ = 10 AI₂ = 25 Ad = 20 cmμ₀ = 4π × 10⁻⁷ T·m/A

F/L = µN/m

5.Hard

In a velocity selector, crossed fields E = 2 × 10⁵ V/m and B = 0.1 T let only ions of one speed pass straight through. Find that speed v.

E = 2 × 10⁵ V/mB₁ = 0.1 T

v = m/s

6.Hard

A long air-core solenoid has 500 turns, a length of 40 cm and a diameter of 2 cm. Find its self-inductance L.

N = 500l = 40 cm⌀ = 2 cmμ₀ = 4π × 10⁻⁷ T·m/A

L = µH

Answer key

1. B = 12.57 µT
2. Φ = 10.39 mWb
3. ε = 6 V
4. F/L = 250 µN/m
5. v = 2 × 10⁶ m/s
6. L = 246.7 µH

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