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
nB37°15 cm × 10 cmB = 0.8 T

A rectangular loop of 15 cm by 10 cm lies in a uniform magnetic field of 0.8 T. The field makes an angle of 37° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.8 TA = 15 cm × 10 cm37° to the normal
Φ = mWb
2.Easy
I = ?Pr = 4 cmB = 50 µT

The magnetic flux density 4 cm from a long straight wire is 50 µT. Find the current I in the wire.

B = 50 µTr = 4 cmμ₀ = 4π × 10⁻⁷ T·m/A
I = A
3.Medium
15 A5 Ad = 12 cmP

Two long parallel wires 12 cm apart carry currents of 15 A and 5 A in the same direction. Find the magnitude of the magnetic flux density B at point P, halfway between them.

I1 = 15 AI2 = 5 Ad = 12 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
4.Medium
R = 10 Ωv = 10 m/sL = 80 cmB = 0.2 T

A metal rod 80 cm long slides at 10 m/s along two rails in a uniform field of 0.2 T into the page. The rails are joined by a resistor of 10 Ω; the rod and rails have negligible resistance. Find the power P dissipated in the resistor.

B = 0.2 TL = 80 cmv = 10 m/sR = 10 Ω
P = mW
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
L1​ = 100 mH500 A/sL2​ = 100 mHk = 0.2ε = ?

Two coils with self-inductances of 100 mH and 100 mH have a coupling coefficient of 0.2. The current in the first coil changes at 500 A/s. Find the emf ε induced in the second coil.

L1 = 100 mHL2 = 100 mHk = 0.2di/dt = 500 A/s
ε = V

Answer key

  1. 1. Φ = 9.584 mWb
  2. 2. I = 10 A
  3. 3. B = 33.33 µT
  4. 4. P = 256 mW
  5. 5. r = 4.569 cm
  6. 6. ε = 10 V

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