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, 20 cm from the wire.

I = 25 Ar = 20 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

2.Easy

An alpha particle moves at 5 × 10⁵ m/s at an angle of 45° to a uniform magnetic field of 0.01 T. Find the magnitude of the magnetic force F on it.

|q| = 3.204 × 10⁻¹⁹ Cv = 5 × 10⁵ m/sB = 0.01 Tθ = 45°

F = fN

3.Medium

A metal rod 30 cm long slides at 8 m/s along two rails in a uniform field of 0.5 T into the page. The rails are joined by a resistor of 4 Ω; the rod and rails have negligible resistance. Find the power P dissipated in the resistor.

B = 0.5 TL = 30 cmv = 8 m/sR = 4 Ω

P = mW

4.Medium

An alpha particle moving at 3 × 10⁶ m/s enters a uniform magnetic field at right angles and moves on a circle of radius 7.777 cm. Find the magnetic flux density B.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ Cv = 3 × 10⁶ m/sr = 7.777 cm

B = T

5.Hard

In a velocity selector, crossed fields E = 4 × 10⁴ V/m and B = 0.05 T let only ions of one speed pass straight through. Find that speed v.

E = 4 × 10⁴ V/mB₁ = 0.05 T

v = m/s

6.Hard

A coil of 50 turns, 10 cm × 25 cm, rotates in a uniform field of 0.3 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 8.33 V?

N = 50A = 10 cm × 25 cmB = 0.3 TE_rms = 8.33 V

n = rpm

Answer key

1. B = 25 µT
2. F = 1.133 fN
3. P = 360 mW
4. B = 0.8 T
5. v = 800000 m/s
6. n = 300 rpm

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