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
nB37°10 cm × 25 cmB = 0.2 T

A rectangular loop of 10 cm by 25 cm lies in a uniform magnetic field of 0.2 T. The field lines make an angle of 53° with the plane of the loop. Find the magnetic flux Φ through the loop.

B = 0.2 TA = 10 cm × 25 cm53° to the plane
Φ = mWb
2.Easy
B0.05 T2 A60°L = 40 cm

A straight wire 40 cm long carries 2 A at an angle of 60° to a uniform magnetic field of 0.05 T. Find the magnitude of the force F on the wire.

B = 0.05 TI = 2 AL = 40 cmθ = 60°
F = N
3.Medium
R = 0.5 Ωv = 5 m/sL = 25 cmB = 0.25 T

A metal rod 25 cm long slides at 5 m/s along two rails in a uniform field of 0.25 T into the page. The rails are joined by a resistor of 0.5 Ω; the rod and rails have negligible resistance. Find the power P dissipated in the resistor.

B = 0.25 TL = 25 cmv = 5 m/sR = 0.5 Ω
P = mW
4.Medium
nBA = 200 cm², N = 250B: 0.05 → 0.85 T

A coil of 250 turns, area 200 cm² and resistance 4 Ω forms a closed circuit. A uniform field perpendicular to the coil rises steadily from 0.05 T to 0.85 T in 500 ms. Find the average induced current I.

N = 250A = 200 cm²B: 0.05 T → 0.85 TΔt = 500 msR = 4 Ω
I = A
5.Hard
Bn = ?15 cm × 5 cmN = 150B = 0.5 T

A coil of 150 turns, 15 cm × 5 cm, rotates in a uniform field of 0.5 T about an axis perpendicular to the field. At what speed n (in revolutions per minute) must it turn to give an rms emf of 12.5 V?

N = 150A = 15 cm × 5 cmB = 0.5 TErms = 12.5 V
n = rpm
6.Hard
V = 1000 VB = 0.5 Tr = ?

An alpha particle starts from rest, is accelerated through a potential difference of 1000 V and then enters a uniform magnetic field of 0.5 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 = 1000 VB = 0.5 T
r = cm

Answer key

  1. 1. Φ = 3.993 mWb
  2. 2. F = 0.03464 N
  3. 3. P = 195.3 mW
  4. 4. I = 2 A
  5. 5. n = 300.1 rpm
  6. 6. r = 1.288 cm

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