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
B = ?I = 1.5 AL = 15 cmN = 1200

A solenoid 15 cm long has 1200 turns and carries 1.5 A. Find the magnetic flux density B inside it, far from the ends.

N = 1200L = 15 cmI = 1.5 Aμ₀ = 4π × 10⁻⁷ T·m/A
B = mT
2.Easy
nB20°15 cm × 30 cmB = 0.05 T

A rectangular loop of 15 cm by 30 cm lies in a uniform magnetic field of 0.05 T. The field makes an angle of 20° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.05 TA = 15 cm × 30 cm20° to the normal
Φ = mWb
3.Medium
R = 4 Ωv = 1 m/sL = 60 cmB = 0.8 T

A metal rod 60 cm long slides at 1 m/s along two rails in a uniform field of 0.8 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 = 0.8 TL = 60 cmv = 1 m/sR = 4 Ω
I = mA
4.Medium
dB/dt > 0I = ?

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

B: into the pagedB/dt > 0
  1. 1clockwise
  2. 2counterclockwise
5.Hard
Bn = ?10 cm × 5 cmN = 200B = 0.05 T

A coil of 200 turns, 10 cm × 5 cm, rotates in a uniform field of 0.05 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 5.554 V?

N = 200A = 10 cm × 5 cmB = 0.05 TErms = 5.554 V
n = rpm
6.Hard
L = 10 mH3.5 → 0.5 A

The current in a 10 mH inductor changes steadily from 3.5 A to 0.5 A in 20 ms. Find the magnitude of the self-induced emf ε.

L = 10 mH3.5 A → 0.5 AΔt = 20 ms
ε = V

Answer key

  1. 1. B = 15.08 mT
  2. 2. Φ = 2.114 mWb
  3. 3. I = 120 mA
  4. 4. counterclockwise
  5. 5. n = 1500 rpm
  6. 6. ε = 1.5 V

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