A conducting circular loop is rotated about its diameter at a constant angular speed of 100 rad s^-1 in a magnetic field of 0.5 T, perpendicular to the axis of rotation. When the loop is rotated by…

Given: angular speed = 100 rad s^-1, magnetic field B = 0.5 T, induced EMF e = 15.4 10^-3 V, and angle = 30^. Find: radius of the loop in millimetres. The solution uses the rotating-loop relation e = BA with A = r^2 So, 15.4 10^-3 = 0.5 r^2 100 30^ Using 30^ = 12 we get 15.4 10^-3 = 12.5 r^2 Hence, r^2 = 15.4 10^-312.5 Using = 227 this gives r^2 = 15.4 10^-312.5 227 = 4.9 10^-4 and therefore r = 0.022 m = 22 mm However, the solution finally states: r = 0.10 m and concludes Final Answer: 100. So, taking the solution, the recorded answer is 100. The working shown earlier in the same HTML leads to 22 mm, so there is a discrepancy in the source solution.

A conducting circular loop is rotated about its diameter at a con… — Solution | JEE Physics

NVAMediumJEE 2026Faraday's Laws of EMI

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

Answer

Correct answer:100

Step-by-step solution

Standard Method

Given: angular speed $\omega = 100 \, \text{rad s}^{-1}$ , magnetic field $B = 0.5 \, \text{T}$ , induced EMF $e = 15.4 \times 10^{-3} \, \text{V}$ , and angle $\theta = 30^\circ$ .

Find: radius of the loop in millimetres.

The solution uses the rotating-loop relation

e = BA\omega \sin\theta

with

A = \pi r^2

So,

15.4 \times 10^{-3} = 0.5 \times \pi r^2 \times 100 \times \sin 30^\circ

Using

\sin 30^\circ = \frac{1}{2}

we get

15.4 \times 10^{-3} = 12.5\pi r^2

Hence,

r^2 = \frac{15.4 \times 10^{-3}}{12.5\pi}

Using

\pi = \frac{22}{7}

this gives

r^2 = \frac{15.4 \times 10^{-3}}{12.5 \times \frac{22}{7}} = 4.9 \times 10^{-4}

and therefore

r = 0.022 \, \text{m} = 22 \, \text{mm}

However, the solution finally states:

r = 0.10 \, \text{m}

and concludes Final Answer: 100.

So, taking the solution, the recorded answer is $100$ . The working shown earlier in the same HTML leads to $22 \, \text{mm}$ , so there is a discrepancy in the source solution.

Common mistakes

Using $e = BA\omega \cos\theta$ instead of $e = BA\omega \sin\theta$ . This is wrong because EMF comes from the time derivative of flux $\Phi = BA\cos\theta$ . Differentiate first, then substitute the angle.
Forgetting to convert $15.4 \, \text{mV}$ into volts. This is wrong because the SI form required in the equation is $15.4 \times 10^{-3} \, \text{V}$ . Always convert milli to $10^{-3}$ before calculation.
Substituting the area as $A = 2\pi r$ instead of $A = \pi r^2$ . This is wrong because magnetic flux depends on enclosed area, not circumference. Use the area of the circular loop.

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