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

An alpha particle moves at 6 × 10⁶ m/s at an angle of 45° to a uniform magnetic field of 0.02 T. Find the magnitude of the magnetic force F on it.

|q| = 3.204 × 10⁻¹⁹ Cv = 6 × 10⁶ m/sB = 0.02 Tθ = 45°

F = fN

2.Easy

A rectangular loop of 12 cm by 15 cm lies in a uniform magnetic field of 0.5 T. The field lines make an angle of 53° with the plane of the loop. Find the magnetic flux Φ through the loop.

B = 0.5 TA = 12 cm × 15 cm53° to the plane

Φ = mWb

3.Medium

A coil of 500 turns has an area of 20 cm². The coil is turned over (rotated through 180°) in a uniform field of 0.2 T, which is perpendicular to its plane, in 40 ms. Find the average induced emf ε.

N = 500A = 20 cm²B = 0.2 TΔt = 40 ms

ε = V

4.Medium

A circular loop lies in a uniform magnetic field pointing into the page. The field strength is decreasing. Click the direction of the induced current in the loop as seen in the drawing.

B: into the pagedB/dt < 0

1clockwise
2counterclockwise

5.Hard

A long air-core solenoid has 300 turns, a length of 50 cm and a diameter of 5 cm. Find the energy W stored in its magnetic field when it carries 1 A.

N = 300l = 50 cm⌀ = 5 cmI = 1 Aμ₀ = 4π × 10⁻⁷ T·m/A

W = µJ

6.Hard

In a velocity selector, crossed fields E = 1 × 10⁵ V/m and B = 0.05 T let only ions of one speed pass straight through. Find that speed v.

E = 1 × 10⁵ V/mB₁ = 0.05 T

v = m/s

Answer key

1. F = 27.19 fN
2. Φ = 7.188 mWb
3. ε = 10 V
4. clockwise
5. W = 222.1 µJ
6. v = 2 × 10⁶ m/s

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