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 ___

Conducting circular loop rotated in magnetic field | JEE Main 2026

Q. A conducting circular loop is rotated about its diameter at a constant angular speed of $100\ \text{rad s}^{-1}$ in a magnetic field of $0.5\ \text{T}$ perpendicular to the axis of rotation. When the loop is rotated by $30^\circ$ from the horizontal position, the induced EMF is $15.4\ \text{mV}$. The radius of the loop is ____ mm.

(Take $\pi=\dfrac{22}{7}$)

Correct Answer: 14 mm

Explanation

Induced EMF in a rotating loop is given by

$$ e = B A \omega \sin\theta $$

Where $A=\pi r^2$

Given:

$$ e = 15.4\times10^{-3}\ \text{V},\quad B = 0.5\ \text{T},\quad \omega = 100\ \text{rad s}^{-1},\quad \theta = 30^\circ $$

Substituting:

$$ 15.4\times10^{-3} = 0.5 \times \pi r^2 \times 100 \times \sin30^\circ $$

$$ 15.4\times10^{-3} = 25\pi r^2 $$

$$ r^2 = \frac{15.4\times10^{-3}}{25\pi} $$

Using $\pi=\dfrac{22}{7}$,

$$ r = 0.014\ \text{m} = 14\ \text{mm} $$

Explanation

Related JEE Main Questions