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 10 cm by 10 cm lies in a uniform magnetic field of 0.3 T. The field lines make an angle of 20° with the plane of the loop. Find the magnetic flux Φ through the loop.

B = 0.3 TA = 10 cm × 10 cm20° to the plane

Φ = mWb

2.Easy

A solenoid 20 cm long carries 3 A. How many turns N must it have for a flux density of 9.425 mT inside?

I = 3 AL = 20 cmB = 9.425 mTμ₀ = 4π × 10⁻⁷ T·m/A

N =

3.Medium

An electron moves at 2 × 10⁶ m/s perpendicular to a uniform magnetic field of 2 mT. Find the radius r of its circular path.

m = 9.109 × 10⁻³¹ kg|q| = 1.602 × 10⁻¹⁹ Cv = 2 × 10⁶ m/sB = 2 mT

r = cm

4.Medium

An alpha particle moves on a circle in a uniform magnetic field of 0.1 T. Find the time T it takes for one revolution.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ CB = 0.1 T

T = ns

5.Hard

A long air-core solenoid has 500 turns, a length of 25 cm and a diameter of 5 cm. Find its self-inductance L.

N = 500l = 25 cm⌀ = 5 cmμ₀ = 4π × 10⁻⁷ T·m/A

L = mH

6.Hard

An alpha particle starts from rest, is accelerated through a potential difference of 5000 V and then enters a uniform magnetic field of 0.8 T at right angles. Find the radius r of its path in the field.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ CV = 5000 VB = 0.8 T

r = cm

Answer key

1. Φ = 1.026 mWb
2. N = 500
3. r = 0.5686 cm
4. T = 1303 ns
5. L = 2.467 mH
6. r = 1.8 cm

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