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
B0.12 TI = ?60°L = 100 cm

A straight wire 100 cm long lies at 60° to a uniform magnetic field of 0.12 T. The magnetic force on it is 0.5196 N. Find the current I.

B = 0.12 TF = 0.5196 NL = 100 cmθ = 60°
I = A
2.Easy
nB15 cm × 30 cmB = 0.3 T

A rectangular loop of 15 cm by 30 cm lies in a uniform magnetic field of 0.3 T. The field makes an angle of 0° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.3 TA = 15 cm × 30 cm0° to the normal
Φ = mWb
3.Medium
vI = ?

A square loop moves to the right into a region with a uniform magnetic field pointing into the page. Click the direction of the induced current in the loop as seen in the drawing, while the loop is entering the field.

B: into the pageentering the field
  1. 1clockwise
  2. 2counterclockwise
4.Medium
nBA = 100 cm², N = 100B = 0.8 T

A coil of 100 turns has an area of 100 cm². The coil sits in a uniform field of 0.8 T perpendicular to its plane, and the field is switched off in 100 ms. Find the average induced emf ε.

N = 100A = 100 cm²B = 0.8 TΔt = 100 ms
ε = V
5.Hard
E = 5 × 10⁵ V/m, B1​ = 0.4 TB2​ = 0.4 Tr = ?

A deuteron passes undeflected through a velocity selector with crossed fields E = 5 × 10⁵ V/m and B₁ = 0.4 T. It then enters a second region with only a magnetic field B₂ = 0.4 T, at right angles. Find the radius r of its path there.

E = 5 × 10⁵ V/mB1 = 0.4 TB2 = 0.4 Tm = 3.344 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ C
r = cm
6.Hard
N1​ = 1000, l = 30 cm20 A/sN2​ = 200Mε = ?

A short coil of 200 turns is wound tightly round the middle of a long solenoid of 1000 turns, length 30 cm and diameter 4 cm. The current in the solenoid changes at 20 A/s. Find the emf ε induced in the short coil.

N1 = 1000N2 = 200l = 30 cm⌀ = 4 cmdi/dt = 20 A/sμ₀ = 4π × 10⁻⁷ T·m/A
ε = mV

Answer key

  1. 1. I = 5 A
  2. 2. Φ = 13.5 mWb
  3. 3. counterclockwise
  4. 4. ε = 8 V
  5. 5. r = 6.523 cm
  6. 6. ε = 21.06 mV

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