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 = 5 AR = 3 cmB = ?

A single circular loop of wire with radius 3 cm carries a current of 5 A. Find the magnetic flux density B at its centre.

N = 1I = 5 AR = 3 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
3.Medium
+v = 5 × 10⁵ m/sr = ?B = 1.5 T

A proton moves at 5 × 10⁵ m/s perpendicular to a uniform magnetic field of 1.5 T. Find the radius r of its circular path.

m = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ Cv = 5 × 10⁵ m/sB = 1.5 T
r = cm
4.Medium
−v = 4 × 10⁶ m/sr = 0.2274 cmB = ?

An electron moving at 4 × 10⁶ m/s enters a uniform magnetic field at right angles and moves on a circle of radius 0.2274 cm. Find the magnetic flux density B.

m = 9.109 × 10⁻³¹ kg|q| = 1.602 × 10⁻¹⁹ Cv = 4 × 10⁶ m/sr = 0.2274 cm
B = mT
5.Hard
Bn = 600 rpm15 cm × 10 cmN = 500B = 0.4 T

A coil of 500 turns, 15 cm × 10 cm, rotates at 600 rpm in a uniform field of 0.4 T about an axis perpendicular to the field. Find the peak emf E0.

N = 500A = 15 cm × 10 cmB = 0.4 Tn = 600 rpm
E0 = V
6.Hard
E = 4 × 10⁴ V/m, B1​ = 0.05 T

In a velocity selector, crossed fields E = 4 × 10⁴ V/m and B = 0.05 T let only ions of one speed pass straight through. Find that speed v.

E = 4 × 10⁴ V/mB1 = 0.05 T
v = m/s

Answer key

  1. 1. B = 100 µT
  2. 2. B = 104.7 µT
  3. 3. r = 0.3481 cm
  4. 4. B = 10 mT
  5. 5. E0 = 188.5 V
  6. 6. v = 800000 m/s

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