JEE Main 2023 — Physics Electromagnetism

2023integermedium

A square shaped coil of area $70{\mathrm{cm}}^{2}$ having $600$ turns rotates in a magnetic field of $0.4\mathrm{Wb}{m}^{–2}$ , about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes $500$ revolution in a minute, the instantaneous emf when the plane of the coil is inclined at $60^{\circ}$ with the field, will be ______ $V$ .

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

Official previous-year question

Held on 1 Feb 2023 · Verified 6 Jul 2026.

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Solution

Given here, $N=600$ , $A=70\times {10}^{-4}{m}^{2}$ , and $B=0.4T$

Angular speed of coil is $\omega =\frac{2\pi n}{60}=\frac{500\times 2\pi }{60}=\frac{100\pi }{6}\mathrm{rad}{s}^{-1}$

Instantaneous emf in coil is given by $\epsilon =-N\frac{d\phi }{dt}$ , where, magnetic flux $\phi =BA\mathrm{cos}\omega t$ and $\omega t=30^{\circ}$ is angle between $A$ and $B$ .

So, $\epsilon =-N\frac{d(BA\mathrm{cos}\omega t)}{dt}=-N(-BA\omega \mathrm{sin}\omega t)=NBA\omega \mathrm{sin}\omega t$

Putting the values, we get

$\epsilon =600\times 70\times {10}^{-4}\times 0.4\times \frac{100\pi }{6}\times \frac{1}{2}$

$=44V$

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Solution

Given here, $N=600$ , $A=70\times {10}^{-4}{m}^{2}$ , and $B=0.4T$

Angular speed of coil is $\omega =\frac{2\pi n}{60}=\frac{500\times 2\pi }{60}=\frac{100\pi }{6}\mathrm{rad}{s}^{-1}$

Instantaneous emf in coil is given by $\epsilon =-N\frac{d\phi }{dt}$ , where, magnetic flux $\phi =BA\mathrm{cos}\omega t$ and $\omega t=30^{\circ}$ is angle between $A$ and $B$ .

So, $\epsilon =-N\frac{d(BA\mathrm{cos}\omega t)}{dt}=-N(-BA\omega \mathrm{sin}\omega t)=NBA\omega \mathrm{sin}\omega t$

Putting the values, we get

$\epsilon =600\times 70\times {10}^{-4}\times 0.4\times \frac{100\pi }{6}\times \frac{1}{2}$

$=44V$

JEE Main 2023 — Physics Electromagnetism

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JEE Main 2023 — Physics Electromagnetism

Did you get this right?

Solution

Your note

JEE Main Electromagnetism in other years

More JEE Main Electromagnetism questions

Other Physics topics for JEE Main

Mechanics

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Electromagnetism