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 = 10 APr = 5 cmB = ?

A long straight wire carries a current of 10 A. Find the magnetic flux density B at point P, 5 cm from the wire.

I = 10 Ar = 5 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
2.Easy
I = 2.5 AR = 8 cmB = ?

A single circular loop of wire with radius 8 cm carries a current of 2.5 A. Find the magnetic flux density B at its centre.

N = 1I = 2.5 AR = 8 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
3.Medium
nBA = 40 cm², N = 100B: 0.1 → 0.2 T

A coil of 100 turns has an area of 40 cm². A uniform field perpendicular to the coil rises steadily from 0.1 T to 0.2 T in 40 ms. Find the average induced emf ε.

N = 100A = 40 cm²B: 0.1 T → 0.2 TΔt = 40 ms
ε = V
4.Medium
R = 0.5 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 0.5 Ω; the rod and rails have negligible resistance. Find the power P dissipated in the resistor.

B = 0.6 TL = 40 cmv = 4 m/sR = 0.5 Ω
P = W
5.Hard
V = 10000 VB = 0.2 Tr = ?

An alpha particle starts from rest, is accelerated through a potential difference of 10000 V and then enters a uniform magnetic field of 0.2 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 = 10000 VB = 0.2 T
r = cm
6.Hard
I = 5 Al = 30 cmN = 300, ⌀ 1.5 cm

A long air-core solenoid has 300 turns, a length of 30 cm and a diameter of 1.5 cm. Find the energy W stored in its magnetic field when it carries 5 A.

N = 300l = 30 cm⌀ = 1.5 cmI = 5 Aμ₀ = 4π × 10⁻⁷ T·m/A
W = µJ

Answer key

  1. 1. B = 40 µT
  2. 2. B = 19.63 µT
  3. 3. ε = 1 V
  4. 4. P = 1.843 W
  5. 5. r = 10.18 cm
  6. 6. W = 832.7 µJ

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