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 8 cm by 25 cm lies in a uniform magnetic field of 0.25 T. The field lines make an angle of 60° with the plane of the loop. Find the magnetic flux Φ through the loop.

B = 0.25 TA = 8 cm × 25 cm60° to the plane

Φ = mWb

2.Easy

An alpha particle moves at 2.5 × 10⁶ m/s at an angle of 30° to a uniform magnetic field of 0.2 T. Find the magnitude of the magnetic force F on it.

|q| = 3.204 × 10⁻¹⁹ Cv = 2.5 × 10⁶ m/sB = 0.2 Tθ = 30°

F = fN

3.Medium

A metal rod 60 cm long slides at 8 m/s along two rails in a uniform field of 0.25 T into the page. The rails are joined by a resistor of 4 Ω; the rod and rails have negligible resistance. Find the current I.

B = 0.25 TL = 60 cmv = 8 m/sR = 4 Ω

I = mA

4.Medium

Two long parallel wires 3 cm apart carry currents of 15 A and 2 A in opposite directions. Find the magnitude of the magnetic flux density B at point P, halfway between them.

I₁ = 15 AI₂ = 2 Ad = 3 cmμ₀ = 4π × 10⁻⁷ T·m/A

B = µT

5.Hard

A long air-core solenoid has 800 turns, a length of 40 cm and a diameter of 5 cm. Find its self-inductance L.

N = 800l = 40 cm⌀ = 5 cmμ₀ = 4π × 10⁻⁷ T·m/A

L = mH

6.Hard

A coil of 20 turns, 5 cm × 10 cm, rotates at 600 rpm in a uniform field of 0.3 T about an axis perpendicular to the field. Find the peak emf E₀.

N = 20A = 5 cm × 10 cmB = 0.3 Tn = 600 rpm

E₀ = V

Answer key

1. Φ = 4.33 mWb
2. F = 80.1 fN
3. I = 300 mA
4. B = 226.7 µT
5. L = 3.948 mH
6. E₀ = 1.885 V

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