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

The magnetic flux density 6 cm from a long straight wire is 33.33 µT. Find the current I in the wire.

B = 33.33 µTr = 6 cmμ₀ = 4π × 10⁻⁷ T·m/A

I = A

2.Easy

A solenoid 10 cm long has 200 turns and carries 5 A. Find the magnetic flux density B inside it, far from the ends.

N = 200L = 10 cmI = 5 Aμ₀ = 4π × 10⁻⁷ T·m/A

B = mT

3.Medium

An electron moves at 6 × 10⁶ m/s perpendicular to a uniform magnetic field of 1 mT. Find the radius r of its circular path.

m = 9.109 × 10⁻³¹ kg|q| = 1.602 × 10⁻¹⁹ Cv = 6 × 10⁶ m/sB = 1 mT

r = cm

4.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 10 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 = 10 Ω

P = mW

5.Hard

A proton starts from rest, is accelerated through a potential difference of 2000 V and then enters a uniform magnetic field of 0.2 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 = 2000 VB = 0.2 T

r = cm

6.Hard

Two coils with self-inductances of 80 mH and 50 mH have a coupling coefficient of 0.4. The current in the first coil changes at 100 A/s. Find the emf ε induced in the second coil.

L₁ = 80 mHL₂ = 50 mHk = 0.4di/dt = 100 A/s

ε = V

Answer key

1. I = 9.999 A
2. B = 12.57 mT
3. r = 3.412 cm
4. P = 144 mW
5. r = 3.232 cm
6. ε = 2.53 V

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