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 = 4.524 mTI = 1.5 AL = 50 cmN = ?

A solenoid 50 cm long carries 1.5 A. How many turns N must it have for a flux density of 4.524 mT inside?

I = 1.5 AL = 50 cmB = 4.524 mTμ₀ = 4π × 10⁻⁷ T·m/A
N =
2.Easy
I = ?Pr = 2 cmB = 200 µT

The magnetic flux density 2 cm from a long straight wire is 200 µT. Find the current I in the wire.

B = 200 µTr = 2 cmμ₀ = 4π × 10⁻⁷ T·m/A
I = A
3.Medium
R = 4 Ωv = 2.5 m/sL = 40 cmB = 0.1 T

A metal rod 40 cm long slides at 2.5 m/s along two rails in a uniform field of 0.1 T into the page. The rails are joined by a resistor of 4 Ω; the rod and rails have negligible resistance. Find the power P dissipated in the resistor.

B = 0.1 TL = 40 cmv = 2.5 m/sR = 4 Ω
P = mW
4.Medium
nBA = 50 cm², N = 20B: 0 → 0.3 T

A coil of 20 turns has an area of 50 cm². A uniform field perpendicular to the coil rises steadily from 0 T to 0.3 T in 250 ms. Find the average induced emf ε.

N = 20A = 50 cm²B: 0 T → 0.3 TΔt = 250 ms
ε = mV
5.Hard
V = 2000 VB = 0.2 Tr = ?

A deuteron starts from rest, is accelerated through a potential difference of 2000 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 = 3.344 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CV = 2000 VB = 0.2 T
r = cm
6.Hard
L = 100 mH1.5 → 0 A

The current in a 100 mH inductor changes steadily from 1.5 A to 0 A in 20 ms. Find the magnitude of the self-induced emf ε.

L = 100 mH1.5 A → 0 AΔt = 20 ms
ε = V

Answer key

  1. 1. N = 1200
  2. 2. I = 20 A
  3. 3. P = 2.5 mW
  4. 4. ε = 120 mV
  5. 5. r = 4.569 cm
  6. 6. ε = 7.5 V

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