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
I = 2 AR = 15 cmB = ?N = 100

A flat circular coil of 100 turns and radius 15 cm carries a current of 2 A. Find the magnetic flux density B at its centre.

N = 100I = 2 AR = 15 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
2.Easy
nB37°20 cm × 30 cmB = 1.2 T

A rectangular loop of 20 cm by 30 cm lies in a uniform magnetic field of 1.2 T. The field makes an angle of 37° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 1.2 TA = 20 cm × 30 cm37° to the normal
Φ = mWb
3.Medium
R = 8 Ωv = 6 m/sL = 100 cmB = 0.1 T

A metal rod 100 cm long slides at 6 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 force F needed to keep the rod moving at constant speed (no friction).

B = 0.1 TL = 100 cmv = 6 m/sR = 8 Ω
F = mN
4.Medium
dB/dt < 0I = ?

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

B: out of the pagedB/dt < 0
  1. 1clockwise
  2. 2counterclockwise
5.Hard
Bn = 3600 rpm12 cm × 20 cmN = 20B = 0.05 T

A coil of 20 turns, 12 cm × 20 cm, rotates at 3600 rpm in a uniform field of 0.05 T about an axis perpendicular to the field. Find the rms value Erms of the emf.

N = 20A = 12 cm × 20 cmB = 0.05 Tn = 3600 rpm
Erms = V
6.Hard
V = 500 VB = 0.5 Tr = ?

An alpha particle starts from rest, is accelerated through a potential difference of 500 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 = 500 VB = 0.5 T
r = cm

Answer key

  1. 1. B = 837.8 µT
  2. 2. Φ = 57.5 mWb
  3. 3. F = 7.5 mN
  4. 4. counterclockwise
  5. 5. Erms = 6.398 V
  6. 6. r = 0.9108 cm

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