A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5 T 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 is ________ mm.

$(Take π = \frac{22}{7})$ [2026]

Question

A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad/s in a magnetic field of 0.5 T 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 is ________ mm.

$(Take π = \frac{22}{7})$ [2026]

Smart Achievers · Accepted Answer

(14)

$E = B ω A \sin ω t$

$15.4 \times 10^{- 3} = \frac{1}{2} \times 100 \times \frac{22}{7} r^{2} \times \frac{1}{2}$

$r = \sqrt{\frac{15.4 \times 28 \times 10^{- 5}}{22}}$

$R = 14 mm$

Solution

Ans.
(14)

$E = B ω A \sin ω t$

$15.4 \times 10^{- 3} = \frac{1}{2} \times 100 \times \frac{22}{7} r^{2} \times \frac{1}{2}$

$r = \sqrt{\frac{15.4 \times 28 \times 10^{- 5}}{22}}$

$R = 14 mm$

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Solution

Ans. (14) E=BωAsinωt 15.4×10-3=12×100×227r2×12 r=15.4×28×10-522 R=14 mm

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Ans.
(14)

$E = B ω A \sin ω t$

$15.4 \times 10^{- 3} = \frac{1}{2} \times 100 \times \frac{22}{7} r^{2} \times \frac{1}{2}$

$r = \sqrt{\frac{15.4 \times 28 \times 10^{- 5}}{22}}$

$R = 14 mm$