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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
B = 5.236 mTI = ?L = 30 cmN = 250

A solenoid 30 cm long has 250 turns. Which current I gives a magnetic flux density of 5.236 mT inside it?

N = 250L = 30 cmB = 5.236 mTμ₀ = 4π × 10⁻⁷ T·m/A
I = A
2.Easy
nB45°5 cm × 10 cmB = 0.3 T

A rectangular loop of 5 cm by 10 cm lies in a uniform magnetic field of 0.3 T. The field makes an angle of 45° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.3 TA = 5 cm × 10 cm45° to the normal
Φ = mWb
3.Medium
R = 4 Ωv = 4 m/sL = 60 cmB = 0.6 T

A metal rod 60 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 4 Ω; the rod and rails have negligible resistance. Find the current I.

B = 0.6 TL = 60 cmv = 4 m/sR = 4 Ω
I = mA
4.Medium
nBA = 100 cm², N = 200B: 0 → 0.3 T

A coil of 200 turns, area 100 cm² and resistance 25 Ω forms a closed circuit. A uniform field perpendicular to the coil rises steadily from 0 T to 0.3 T in 20 ms. Find the average induced current I.

N = 200A = 100 cm²B: 0 T → 0.3 TΔt = 20 msR = 25 Ω
I = A
5.Hard
L1​ = 10 mH500 A/sL2​ = 100 mHk = 0.6ε = ?

Two coils with self-inductances of 10 mH and 100 mH have a coupling coefficient of 0.6. The current in the first coil changes at 500 A/s. Find the emf ε induced in the second coil.

L1 = 10 mHL2 = 100 mHk = 0.6di/dt = 500 A/s
ε = V
6.Hard
V = 10000 VB = 0.5 Tr = ?

A proton starts from rest, is accelerated through a potential difference of 10000 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 = 10000 VB = 0.5 T
r = cm

Answer key

  1. 1. I = 5 A
  2. 2. Φ = 1.061 mWb
  3. 3. I = 360 mA
  4. 4. I = 1.2 A
  5. 5. ε = 9.487 V
  6. 6. r = 2.89 cm

Full step-by-step solutions: practise this topic on examproblems.com.