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 30 cm lies in a uniform magnetic field of 0.8 T. The field lines make an angle of 20° with the plane of the loop. Find the magnetic flux Φ through the loop.

B = 0.8 TA = 15 cm × 30 cm20° to the plane

Φ = mWb

2.Easy

A straight wire 15 cm long carries 15 A at an angle of 30° to a uniform magnetic field of 0.08 T. Find the magnitude of the force F on the wire.

B = 0.08 TI = 15 AL = 15 cmθ = 30°

F = N

3.Medium

A metal rod 100 cm long slides at 2.5 m/s along two rails in a uniform field of 0.4 T into the page. The rails are joined by a resistor of 1 Ω; the rod and rails have negligible resistance. Find the current I.

B = 0.4 TL = 100 cmv = 2.5 m/sR = 1 Ω

I = A

4.Medium

A coil of 50 turns has an area of 20 cm². A uniform field perpendicular to the coil rises steadily from 0.2 T to 0.3 T in 250 ms. Find the average induced emf ε.

N = 50A = 20 cm²B: 0.2 T → 0.3 TΔt = 250 ms

ε = mV

5.Hard

The current in a 50 mH inductor changes steadily from 5 A to 0 A in 20 ms. Find the magnitude of the self-induced emf ε.

L = 50 mH5 A → 0 AΔt = 20 ms

ε = V

6.Hard

A coil of 50 turns, 15 cm × 25 cm, rotates in a uniform field of 0.5 T about an axis perpendicular to the field. At what speed n (in revolutions per minute) must it turn to give an rms emf of 104.1 V?

N = 50A = 15 cm × 25 cmB = 0.5 TE_rms = 104.1 V

n = rpm

Answer key

1. Φ = 12.31 mWb
2. F = 0.09 N
3. I = 1 A
4. ε = 40 mV
5. ε = 12.5 V
6. n = 1500 rpm

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