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
B0.2 T12 A90°L = 30 cm

A straight wire 30 cm long carries 12 A at an angle of 90° to a uniform magnetic field of 0.2 T. Find the magnitude of the force F on the wire.

B = 0.2 TI = 12 AL = 30 cmθ = 90°
F = N
2.Easy
B = 15.71 mTI = ?L = 12 cmN = 1500

A solenoid 12 cm long has 1500 turns. Which current I gives a magnetic flux density of 15.71 mT inside it?

N = 1500L = 12 cmB = 15.71 mTμ₀ = 4π × 10⁻⁷ T·m/A
I = A
3.Medium
nBA = 150 cm², N = 200B = 0.8 T

A coil of 200 turns has an area of 150 cm². The coil is turned over (rotated through 180°) in a uniform field of 0.8 T, which is perpendicular to its plane, in 200 ms. Find the average induced emf ε.

N = 200A = 150 cm²B = 0.8 TΔt = 200 ms
ε = V
4.Medium
R = 8 Ωv = 2.5 m/sL = 50 cmB = 0.1 T

A metal rod 50 cm long slides at 2.5 m/s along two rails in a uniform field of 0.1 T into the page. The rails are joined by a resistor of 8 Ω; the rod and rails have negligible resistance. Find the power P dissipated in the resistor.

B = 0.1 TL = 50 cmv = 2.5 m/sR = 8 Ω
P = mW
5.Hard
Bn = 3600 rpm20 cm × 5 cmN = 150B = 0.1 T

A coil of 150 turns, 20 cm × 5 cm, rotates at 3600 rpm in a uniform field of 0.1 T about an axis perpendicular to the field. Find the rms value Erms of the emf.

N = 150A = 20 cm × 5 cmB = 0.1 Tn = 3600 rpm
Erms = V
6.Hard
E = 1 × 10⁴ V/m, B1​ = 0.05 TB2​ = 0.8 Tr = ?

A proton passes undeflected through a velocity selector with crossed fields E = 1 × 10⁴ V/m and B₁ = 0.05 T. It then enters a second region with only a magnetic field B₂ = 0.8 T, at right angles. Find the radius r of its path there.

E = 1 × 10⁴ V/mB1 = 0.05 TB2 = 0.8 Tm = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ C
r = cm

Answer key

  1. 1. F = 0.72 N
  2. 2. I = 1 A
  3. 3. ε = 24 V
  4. 4. P = 1.953 mW
  5. 5. Erms = 39.99 V
  6. 6. r = 0.2611 cm

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