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
B = 7.54 mTI = 2 AL = 40 cmN = ?

A solenoid 40 cm long carries 2 A. How many turns N must it have for a flux density of 7.54 mT inside?

I = 2 AL = 40 cmB = 7.54 mTμ₀ = 4π × 10⁻⁷ T·m/A
N =
2.Easy
nB60°5 cm × 10 cmB = 0.2 T

A rectangular loop of 5 cm by 10 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 = 5 cm × 10 cm60° to the normal
Φ = mWb
3.Medium
−vBF = ?

An electron moves down the page through a uniform magnetic field pointing out of the page. Click the direction of the magnetic force on it.

v: down the pageB: out of the page
  1. 1up the page
  2. 2to the right
  3. 3down the page
  4. 4to the left
4.Medium
R = 1 Ωv = 1 m/sL = 40 cmB = 0.4 T

A metal rod 40 cm long slides at 1 m/s along two rails in a uniform field of 0.4 T into the page. Find the induced emf ε between its ends.

B = 0.4 TL = 40 cmv = 1 m/s
ε = mV
5.Hard
E = 5 × 10⁵ V/m, B1​ = 0.05 TB2​ = 0.8 Tr = ?

A proton passes undeflected through a velocity selector with crossed fields E = 5 × 10⁵ V/m and B₁ = 0.05 T. It then enters a second region with only a magnetic field B₂ = 0.8 T, at right angles. Find the radius r of its path there.

E = 5 × 10⁵ V/mB1 = 0.05 TB2 = 0.8 Tm = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ C
r = cm
6.Hard
Bn = 300 rpm8 cm × 5 cmN = 500B = 0.05 T

A coil of 500 turns, 8 cm × 5 cm, rotates at 300 rpm in a uniform field of 0.05 T about an axis perpendicular to the field. Find the peak emf E0.

N = 500A = 8 cm × 5 cmB = 0.05 Tn = 300 rpm
E0 = V

Answer key

  1. 1. N = 1200
  2. 2. Φ = 0.5 mWb
  3. 3. to the right
  4. 4. ε = 160 mV
  5. 5. r = 13.05 cm
  6. 6. E0 = 3.142 V

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