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 long straight wire carries a current of 25 A. Find the magnetic flux density B at point P, 2.5 cm from the wire.

I = 25 Ar = 2.5 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

2.Easy

A rectangular loop of 15 cm by 10 cm lies in a uniform magnetic field of 0.3 T. The field makes an angle of 37° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.3 TA = 15 cm × 10 cm37° to the normal

Φ = mWb

3.Medium

A coil of 20 turns has an area of 80 cm². A uniform field perpendicular to the coil rises steadily from 0.05 T to 0.85 T in 10 ms. Find the average induced emf ε.

N = 20A = 80 cm²B: 0.05 T → 0.85 TΔt = 10 ms

ε = V

4.Medium

Two long parallel wires 3 cm apart carry currents of 2 A and 8 A in opposite directions. Find the magnitude of the magnetic flux density B at point P, halfway between them.

I₁ = 2 AI₂ = 8 Ad = 3 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

5.Hard

A long air-core solenoid has 100 turns, a length of 10 cm and a diameter of 1.5 cm. Find its self-inductance L.

N = 100l = 10 cm⌀ = 1.5 cmμ₀ = 4π × 10⁻⁷ T·m/A

L = µH

6.Hard

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. B = 200 µT
2. Φ = 3.594 mWb
3. ε = 12.8 V
4. B = 133.3 µT
5. L = 22.21 µH
6. v = 1 × 10⁶ m/s

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