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 solenoid 50 cm long has 1500 turns. Which current I gives a magnetic flux density of 18.85 mT inside it?

N = 1500L = 50 cmB = 18.85 mTμ₀ = 4π × 10⁻⁷ T·m/A

I = A

2.Easy

A rectangular loop of 15 cm by 30 cm lies in a uniform magnetic field of 0.05 T. The field lines make an angle of 53° with the plane of the loop. Find the magnetic flux Φ through the loop.

B = 0.05 TA = 15 cm × 30 cm53° to the plane

Φ = mWb

3.Medium

Two long parallel wires 12 cm apart carry currents of 30 A and 20 A in the same direction. Find the force per metre of length F/L between them.

I₁ = 30 AI₂ = 20 Ad = 12 cmμ₀ = 4π × 10⁻⁷ T·m/A

F/L = µN/m

4.Medium

An electron moving at 1.5 × 10⁶ m/s enters a uniform magnetic field at right angles and moves on a circle of radius 0.4265 cm. Find the magnetic flux density B.

m = 9.109 × 10⁻³¹ kg|q| = 1.602 × 10⁻¹⁹ Cv = 1.5 × 10⁶ m/sr = 0.4265 cm

B = mT

5.Hard

A coil of 20 turns, 8 cm × 10 cm, rotates at 1800 rpm in a uniform field of 0.5 T about an axis perpendicular to the field. Find the rms value E_rms of the emf.

N = 20A = 8 cm × 10 cmB = 0.5 Tn = 1800 rpm

E_rms = V

6.Hard

In a velocity selector, crossed fields E = 5 × 10⁵ V/m and B = 0.05 T let only ions of one speed pass straight through. Find that speed v.

E = 5 × 10⁵ V/mB₁ = 0.05 T

v = m/s

Answer key

1. I = 5 A
2. Φ = 1.797 mWb
3. F/L = 1000 µN/m
4. B = 2 mT
5. E_rms = 10.66 V
6. v = 1 × 10⁷ m/s

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