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 = 4 APr = ?B = 5.333 µT

A long straight wire carries 4 A. At what distance r from the wire is the magnetic flux density 5.333 µT?

I = 4 AB = 5.333 µTμ₀ = 4π × 10⁻⁷ T·m/A
r = cm
2.Easy
nB60°10 cm × 30 cmB = 0.2 T

A rectangular loop of 10 cm by 30 cm lies in a uniform magnetic field of 0.2 T. The field makes an angle of 60° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.2 TA = 10 cm × 30 cm60° to the normal
Φ = mWb
3.Medium
−v = 1 × 10⁶ m/sr = ?B = 2.5 mT

An electron moves at 1 × 10⁶ m/s perpendicular to a uniform magnetic field of 2.5 mT. Find the radius r of its circular path.

m = 9.109 × 10⁻³¹ kg|q| = 1.602 × 10⁻¹⁹ Cv = 1 × 10⁶ m/sB = 2.5 mT
r = cm
4.Medium
R = 0.5 Ωv = 8 m/sL = 80 cmB = 1 T

A metal rod 80 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 0.5 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 = 80 cmv = 8 m/sR = 0.5 Ω
F = N
5.Hard
V = 2500 VB = 0.5 Tr = ?

An alpha particle starts from rest, is accelerated through a potential difference of 2500 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 = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ CV = 2500 VB = 0.5 T
r = cm
6.Hard
V = 5000 VB = 0.25 Tr = ?

A deuteron starts from rest, is accelerated through a potential difference of 5000 V and then enters a uniform magnetic field of 0.25 T at right angles. Find the radius r of its path in the field.

m = 3.344 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CV = 5000 VB = 0.25 T
r = cm

Answer key

  1. 1. r = 15 cm
  2. 2. Φ = 3 mWb
  3. 3. r = 0.2274 cm
  4. 4. F = 10.24 N
  5. 5. r = 2.037 cm
  6. 6. r = 5.779 cm

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