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 = 3.142 mTI = 5 AL = 50 cmN = ?

A solenoid 50 cm long carries 5 A. How many turns N must it have for a flux density of 3.142 mT inside?

I = 5 AL = 50 cmB = 3.142 mTμ₀ = 4π × 10⁻⁷ T·m/A
N =
2.Easy
nB30°20 cm × 20 cmB = 0.05 T

A rectangular loop of 20 cm by 20 cm lies in a uniform magnetic field of 0.05 T. The field makes an angle of 30° with the normal of the loop. Find the magnetic flux Φ through the loop.

B = 0.05 TA = 20 cm × 20 cm30° to the normal
Φ = mWb
3.Medium
nBA = 25 cm², N = 20B = 0.4 T

A coil of 20 turns has an area of 25 cm². The coil sits in a uniform field of 0.4 T perpendicular to its plane, and the field is switched off in 100 ms. Find the average induced emf ε.

N = 20A = 25 cm²B = 0.4 TΔt = 100 ms
ε = mV
4.Medium
+v = 4 × 10⁵ m/sB = 0.1 T

An alpha particle moves on a circle in a uniform magnetic field of 0.1 T. Find the time T it takes for one revolution.

m = 6.645 × 10⁻²⁷ kg|q| = 3.204 × 10⁻¹⁹ CB = 0.1 T
T = ns
5.Hard
V = 1000 VB = 0.3 Tr = ?

An alpha particle starts from rest, is accelerated through a potential difference of 1000 V and then enters a uniform magnetic field of 0.3 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 = 1000 VB = 0.3 T
r = cm
6.Hard
N1​ = 500, l = 50 cm500 A/sN2​ = 200Mε = ?

A short coil of 200 turns is wound tightly round the middle of a long solenoid of 500 turns, length 50 cm and diameter 4 cm. The current in the solenoid changes at 500 A/s. Find the emf ε induced in the short coil.

N1 = 500N2 = 200l = 50 cm⌀ = 4 cmdi/dt = 500 A/sμ₀ = 4π × 10⁻⁷ T·m/A
ε = mV

Answer key

  1. 1. N = 250
  2. 2. Φ = 1.732 mWb
  3. 3. ε = 200 mV
  4. 4. T = 1303 ns
  5. 5. r = 2.147 cm
  6. 6. ε = 157.9 mV

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