Question
GeneralGeneralGeneral

A conducting circular loop rotates with angular speed 100 rad/s in magnetic field 0.5 T. When rotated by 30°, induced EMF is 15.4 mV. Find radius of loop.

Verified Answer

Solution:

Induced EMF:

E = BAω sinθ

Where:

  • E = 15.4 × 10-3 V
  • B = 0.5 T
  • ω = 100 rad/s
  • θ = 30°

15.4 × 10-3 = 0.5 × A × 100 × (1/2)

15.4 × 10-3 = 25A

A = 6.16 × 10-4 m2

For circular loop:

A = πr2

r = √(A/π)

r = √[(6.16 × 10-4)/π]

r ≈ 1.4 × 10-2 m

r ≈ 1.4 cm

Answer: 1.4 cm