A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5T perpendicular to the axis of rotation. When the loop is rotated by 30° from the horizontal position, the induced EMF is 15.4 mV. The radius of the loop i $s ______$ mm.
(Take π = 22/7)

Question

A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5T perpendicular to the axis of rotation. When the loop is rotated by 30° from the horizontal position, the induced EMF is 15.4 mV. The radius of the loop i $s ______$ mm.

(Take π = 22/7)

G1 Physics · Accepted Answer

For a rotating conducting loop, ε = BωA sinθ. Here, B = 0.5 T, ω = 100 rad/s, θ = 30°, ε = 15.4 mV = 15.4 × 10⁻³ V. The loop area is A = πr². Therefore, 15.4 × 10⁻³ = 0.5 × 100 × πr² × sin30°. Since sin30° = 1/2, 15.4 × 10⁻³ = 25πr². Thus, r² = (15.4 × 10⁻³)/(25π). Using π = 22/7, r² = 1.96 × 10⁻⁴ m². Hence, r = 0.014 m = 14 mm. Therefore the answer is 14.