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 = 5 APr = 4 cmB = ?

A long straight wire carries a current of 5 A. Find the magnetic flux density B at point P, 4 cm from the wire.

I = 5 Ar = 4 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
2.Easy
B = ?I = 0.5 AL = 40 cmN = 1000

A solenoid 40 cm long has 1000 turns and carries 0.5 A. Find the magnetic flux density B inside it, far from the ends.

N = 1000L = 40 cmI = 0.5 Aμ₀ = 4π × 10⁻⁷ T·m/A
B = mT
3.Medium
nBA = 20 cm², N = 20B: 0.2 → 0.5 T

A coil of 20 turns has an area of 20 cm². A uniform field perpendicular to the coil rises steadily from 0.2 T to 0.5 T in 10 ms. Find the average induced emf ε.

N = 20A = 20 cm²B: 0.2 T → 0.5 TΔt = 10 ms
ε = V
4.Medium
dB/dt < 0I = ?

A circular loop lies in a uniform magnetic field pointing into the page. The field strength is decreasing. 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
L1​ = 80 mH20 A/sL2​ = 50 mHk = 0.75ε = ?

Two coils with self-inductances of 80 mH and 50 mH have a coupling coefficient of 0.75. The current in the first coil changes at 20 A/s. Find the emf ε induced in the second coil.

L1 = 80 mHL2 = 50 mHk = 0.75di/dt = 20 A/s
ε = V
6.Hard
V = 2000 VB = 0.5 Tr = ?

A proton starts from rest, is accelerated through a potential difference of 2000 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 = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CV = 2000 VB = 0.5 T
r = cm

Answer key

  1. 1. B = 25 µT
  2. 2. B = 1.571 mT
  3. 3. ε = 1.2 V
  4. 4. clockwise
  5. 5. ε = 0.9487 V
  6. 6. r = 1.293 cm

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