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 30 cm long carries 0.5 A. How many turns N must it have for a flux density of 1.676 mT inside?

I = 0.5 AL = 30 cmB = 1.676 mTμ₀ = 4π × 10⁻⁷ T·m/A

N =

2.Easy

A solenoid 20 cm long has 1000 turns. Which current I gives a magnetic flux density of 12.57 mT inside it?

N = 1000L = 20 cmB = 12.57 mTμ₀ = 4π × 10⁻⁷ T·m/A

I = A

3.Medium

A metal rod 40 cm long slides at 8 m/s along two rails in a uniform field of 0.1 T into the page. The rails are joined by a resistor of 2.5 Ω; the rod and rails have negligible resistance. Find the power P dissipated in the resistor.

B = 0.1 TL = 40 cmv = 8 m/sR = 2.5 Ω

P = mW

4.Medium

An electron moves at 6 × 10⁶ m/s perpendicular to a uniform magnetic field of 4 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 = 4 mT

r = cm

5.Hard

A short coil of 50 turns is wound tightly round the middle of a long solenoid of 2000 turns, length 20 cm and diameter 2 cm. Find their mutual inductance M.

N₁ = 2000N₂ = 50l = 20 cm⌀ = 2 cmμ₀ = 4π × 10⁻⁷ T·m/A

M = µH

6.Hard

A deuteron starts from rest, is accelerated through a potential difference of 1000 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 = 3.344 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CV = 1000 VB = 0.8 T

r = cm

Answer key

1. N = 800.2
2. I = 2.001 A
3. P = 40.96 mW
4. r = 0.8529 cm
5. M = 197.4 µH
6. r = 0.8077 cm

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