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 = ?I = 2 AL = 20 cmN = 400

A solenoid 20 cm long has 400 turns and carries 2 A. Find the magnetic flux density B inside it, far from the ends.

N = 400L = 20 cmI = 2 Aμ₀ = 4π × 10⁻⁷ T·m/A
B = mT
2.Easy
I = 25 APr = 12 cmB = ?

A long straight wire carries a current of 25 A. Find the magnetic flux density B at point P, 12 cm from the wire.

I = 25 Ar = 12 cmμ₀ = 4π × 10⁻⁷ T·m/A
B = µT
3.Medium
nBA = 50 cm², N = 250B = 0.1 T

A coil of 250 turns has an area of 50 cm². The coil is turned over (rotated through 180°) in a uniform field of 0.1 T, which is perpendicular to its plane, in 40 ms. Find the average induced emf ε.

N = 250A = 50 cm²B = 0.1 TΔt = 40 ms
ε = V
4.Medium
vI = ?

A square loop moves to the right into a region with a uniform magnetic field pointing out of 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: out of the pageentering the field
  1. 1clockwise
  2. 2counterclockwise
5.Hard
Bn = ?15 cm × 5 cmN = 50B = 0.2 T

A coil of 50 turns, 15 cm × 5 cm, rotates in a uniform field of 0.2 T about an axis perpendicular to the field. At what speed n (in revolutions per minute) must it turn to give an rms emf of 9.996 V?

N = 50A = 15 cm × 5 cmB = 0.2 TErms = 9.996 V
n = rpm
6.Hard
V = 5000 VB = 0.25 Tr = ?

A proton 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 = 1.673 × 10⁻²⁷ kg|q| = 1.602 × 10⁻¹⁹ CV = 5000 VB = 0.25 T
r = cm

Answer key

  1. 1. B = 5.027 mT
  2. 2. B = 41.67 µT
  3. 3. ε = 6.25 V
  4. 4. clockwise
  5. 5. n = 1800 rpm
  6. 6. r = 4.088 cm

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