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 = 22/7) Numerical answer type. Work it out, then open the answer.

Answer: 14. Starting from the horizontal position (plane perpendicular to B): e = BAωsin θ. At θ = 30°: 15.4×10⁻³ = 0.5 × π r² × 100 × 1/2 = 25π r² π r² = 6.16×10⁻⁴ ⇒ r² = 6.16×10⁻⁴ × 7/22 = 1.96×10⁻⁴ m² r = 1.4×10⁻² m = 14 mm

A conducting circular loop is rotated about its diameter at a… | JEE Main 2026 (22 Jan, Shift 2)

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Rotating Conductors & AC Generator

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

Numerical answer type. Work it out, then open the answer.

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Answer: 14

Starting from the horizontal position (plane perpendicular to $B$ ): $e = BA\omega\sin\theta$ .
At $\theta = 30^\circ$ : $15.4\times10^{-3} = 0.5 \times \pi r^2 \times 100 \times \frac{1}{2} = 25\pi r^2$
$\pi r^2 = 6.16\times10^{-4} \Rightarrow r^2 = 6.16\times10^{-4} \times \frac{7}{22} = 1.96\times10^{-4}\text{ m}^2$
$r = 1.4\times10^{-2}\text{ m} = 14\text{ mm}$

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