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 = 37.7 mTI = ?L = 20 cmN = 1500

A solenoid 20 cm long has 1500 turns. Which current I gives a magnetic flux density of 37.7 mT inside it?

N = 1500L = 20 cmB = 37.7 mTμ₀ = 4π × 10⁻⁷ T·m/A
I = A
2.Easy
B = ?I = 3 AL = 30 cmN = 250

A solenoid 30 cm long has 250 turns and carries 3 A. Find the magnetic flux density B inside it, far from the ends.

N = 250L = 30 cmI = 3 Aμ₀ = 4π × 10⁻⁷ T·m/A
B = mT
3.Medium
nBA = 20 cm², N = 200B = 0.3 T

A coil of 200 turns has an area of 20 cm². The coil sits in a uniform field of 0.3 T perpendicular to its plane, and the field is switched off in 500 ms. Find the average induced emf ε.

N = 200A = 20 cm²B = 0.3 TΔt = 500 ms
ε = mV
4.Medium
+vBF = ?

A proton moves up the page through a uniform magnetic field pointing out of the page. Click the direction of the magnetic force on it.

v: up the pageB: out of the page
  1. 1up the page
  2. 2to the right
  3. 3down the page
  4. 4to the left
5.Hard
Bn = 300 rpm5 cm × 20 cmN = 100B = 0.3 T

A coil of 100 turns, 5 cm × 20 cm, rotates at 300 rpm in a uniform field of 0.3 T about an axis perpendicular to the field. Find the peak emf E0.

N = 100A = 5 cm × 20 cmB = 0.3 Tn = 300 rpm
E0 = V
6.Hard
E = 2 × 10⁵ V/m, B1​ = 0.4 TB2​ = 0.5 Tr = ?

A proton passes undeflected through a velocity selector with crossed fields E = 2 × 10⁵ V/m and B₁ = 0.4 T. It then enters a second region with only a magnetic field B₂ = 0.5 T, at right angles. Find the radius r of its path there.

E = 2 × 10⁵ V/mB1 = 0.4 TB2 = 0.5 Tm = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ C
r = cm

Answer key

  1. 1. I = 4 A
  2. 2. B = 3.142 mT
  3. 3. ε = 240 mV
  4. 4. to the right
  5. 5. E0 = 9.425 V
  6. 6. r = 1.044 cm

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