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 = 2.513 mTI = 0.5 AL = 30 cmN = ?

A solenoid 30 cm long carries 0.5 A. How many turns N must it have for a flux density of 2.513 mT inside?

I = 0.5 AL = 30 cmB = 2.513 mTμ₀ = 4π × 10⁻⁷ T·m/A
N =
2.Easy
I = 1 AR = 4 cmB = ?N = 50

A flat circular coil of 50 turns and radius 4 cm carries a current of 1 A. Find the magnetic flux density B at its centre.

N = 50I = 1 AR = 4 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
3.Medium
nBA = 200 cm², N = 25B: 0.05 → 0.65 T

A coil of 25 turns, area 200 cm² and resistance 20 Ω forms a closed circuit. A uniform field perpendicular to the coil rises steadily from 0.05 T to 0.65 T in 50 ms. Find the average induced current I.

N = 25A = 200 cm²B: 0.05 T → 0.65 TΔt = 50 msR = 20 Ω
I = mA
4.Medium
R = 2.5 Ωv = 4 m/sL = 40 cmB = 0.6 T

A metal rod 40 cm long slides at 4 m/s along two rails in a uniform field of 0.6 T into the page. The rails are joined by a resistor of 2.5 Ω; the rod and rails have negligible resistance. Find the current I.

B = 0.6 TL = 40 cmv = 4 m/sR = 2.5 Ω
I = mA
5.Hard
Bn = ?12 cm × 20 cmN = 200B = 0.5 T

A coil of 200 turns, 12 cm × 20 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 53.31 V?

N = 200A = 12 cm × 20 cmB = 0.5 TErms = 53.31 V
n = rpm
6.Hard
V = 1000 VB = 0.25 Tr = ?

A proton starts from rest, is accelerated through a potential difference of 1000 V and then enters a uniform magnetic field of 0.25 T at right angles. Find the radius r of its path in the field.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CV = 1000 VB = 0.25 T
r = cm

Answer key

  1. 1. N = 1200
  2. 2. B = 785.4 µT
  3. 3. I = 300 mA
  4. 4. I = 384 mA
  5. 5. n = 300 rpm
  6. 6. r = 1.828 cm

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