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 = 3.016 mTI = ?L = 50 cmN = 400

A solenoid 50 cm long has 400 turns. Which current I gives a magnetic flux density of 3.016 mT inside it?

N = 400L = 50 cmB = 3.016 mTμ₀ = 4π × 10⁻⁷ T·m/A
I = A
2.Easy
nB53°5 cm × 20 cmB = 0.25 T

A rectangular loop of 5 cm by 20 cm lies in a uniform magnetic field of 0.25 T. The field makes an angle of 53° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.25 TA = 5 cm × 20 cm53° to the normal
Φ = mWb
3.Medium
30 A8 Ad = 15 cmP

Two long parallel wires 15 cm apart carry currents of 30 A and 8 A in opposite directions. Find the magnitude of the magnetic flux density B at point P, halfway between them.

I1 = 30 AI2 = 8 Ad = 15 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
4.Medium
R = 2.5 Ωv = 8 m/sL = 50 cmB = 1 T

A metal rod 50 cm long slides at 8 m/s along two rails in a uniform field of 1 T into the page. The rails are joined by a resistor of 2.5 Ω; the rod and rails have negligible resistance. Find the force F needed to keep the rod moving at constant speed (no friction).

B = 1 TL = 50 cmv = 8 m/sR = 2.5 Ω
F = mN
5.Hard
Bn = ?10 cm × 5 cmN = 200B = 0.05 T

A coil of 200 turns, 10 cm × 5 cm, rotates in a uniform field of 0.05 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 3.332 V?

N = 200A = 10 cm × 5 cmB = 0.05 TErms = 3.332 V
n = rpm
6.Hard
l = 30 cmN = 400, ⌀ 1 cm

A long air-core solenoid has 400 turns, a length of 30 cm and a diameter of 1 cm. Find its self-inductance L.

N = 400l = 30 cm⌀ = 1 cmμ₀ = 4π × 10⁻⁷ T·m/A
L = µH

Answer key

  1. 1. I = 3 A
  2. 2. Φ = 1.505 mWb
  3. 3. B = 101.3 µT
  4. 4. F = 800 mN
  5. 5. n = 900 rpm
  6. 6. L = 52.64 µH

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