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
nB45°20 cm × 30 cmB = 0.1 T

A rectangular loop of 20 cm by 30 cm lies in a uniform magnetic field of 0.1 T. The field lines make an angle of 45° with the plane of the loop. Find the magnetic flux Φ through the loop.

B = 0.1 TA = 20 cm × 30 cm45° to the plane
Φ = mWb
2.Easy
I = 3 AR = 15 cmB = ?N = 10

A flat circular coil of 10 turns and radius 15 cm carries a current of 3 A. Find the magnetic flux density B at its centre.

N = 10I = 3 AR = 15 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
3.Medium
dB/dt < 0I = ?

A circular loop lies in a uniform magnetic field pointing into the page. The field strength is decreasing. Click the direction of the induced current in the loop as seen in the drawing.

B: into the pagedB/dt < 0
  1. 1clockwise
  2. 2counterclockwise
4.Medium
−v = 4 × 10⁶ m/sr = ?B = 4 mT

An electron moves at 4 × 10⁶ m/s perpendicular to a uniform magnetic field of 4 mT. Find the radius r of its circular path.

m = 9.109 × 10⁻³¹ kg|q| = 1.602 × 10⁻¹⁹ Cv = 4 × 10⁶ m/sB = 4 mT
r = cm
5.Hard
E = 5 × 10⁴ V/m, B1​ = 0.2 TB2​ = 0.25 Tr = ?

An alpha particle passes undeflected through a velocity selector with crossed fields E = 5 × 10⁴ V/m and B₁ = 0.2 T. It then enters a second region with only a magnetic field B₂ = 0.25 T, at right angles. Find the radius r of its path there.

E = 5 × 10⁴ V/mB1 = 0.2 TB2 = 0.25 Tm = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ C
r = cm
6.Hard
Bn = 300 rpm5 cm × 10 cmN = 200B = 0.4 T

A coil of 200 turns, 5 cm × 10 cm, rotates at 300 rpm in a uniform field of 0.4 T about an axis perpendicular to the field. Find the peak emf E0.

N = 200A = 5 cm × 10 cmB = 0.4 Tn = 300 rpm
E0 = V

Answer key

  1. 1. Φ = 4.243 mWb
  2. 2. B = 125.7 µT
  3. 3. clockwise
  4. 4. r = 0.5686 cm
  5. 5. r = 2.074 cm
  6. 6. E0 = 12.57 V

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