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
I = 25 APr = 5 cmB = ?

A long straight wire carries a current of 25 A. Find the magnetic flux density B at point P, 5 cm from the wire.

I = 25 Ar = 5 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
2.Easy
I = 4 AR = 12 cmB = ?N = 10

A flat circular coil of 10 turns and radius 12 cm carries a current of 4 A. Find the magnetic flux density B at its centre.

N = 10I = 4 AR = 12 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
3.Medium
+v = 6 × 10⁵ m/sr = 0.4177 cmB = ?

A proton moving at 6 × 10⁵ m/s enters a uniform magnetic field at right angles and moves on a circle of radius 0.4177 cm. Find the magnetic flux density B.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ Cv = 6 × 10⁵ m/sr = 0.4177 cm
B = T
4.Medium
dB/dt < 0I = ?

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

B: out of the pagedB/dt < 0
  1. 1clockwise
  2. 2counterclockwise
5.Hard
E = 4 × 10⁴ V/m, B1​ = 0.05 TB2​ = 0.2 Tr = ?

An alpha particle passes undeflected through a velocity selector with crossed fields E = 4 × 10⁴ V/m and B₁ = 0.05 T. It then enters a second region with only a magnetic field B₂ = 0.2 T, at right angles. Find the radius r of its path there.

E = 4 × 10⁴ V/mB1 = 0.05 TB2 = 0.2 Tm = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ C
r = cm
6.Hard
Bn = ?5 cm × 20 cmN = 150B = 0.05 T

A coil of 150 turns, 5 cm × 20 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 19.99 V?

N = 150A = 5 cm × 20 cmB = 0.05 TErms = 19.99 V
n = rpm

Answer key

  1. 1. B = 100 µT
  2. 2. B = 209.4 µT
  3. 3. B = 1.5 T
  4. 4. counterclockwise
  5. 5. r = 8.296 cm
  6. 6. n = 3599 rpm

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