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  4. A planar loop of wire rotates in a uniform magnetic field. Initially, at t = 0, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of 10 s about an axis in its plane then the magnitude of induced emf w ill be maximum and minimum, respectively at :

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Q. A planar loop of wire rotates in a uniform magnetic field. Initially, at $t = 0$, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of $10\, s$ about an axis in its plane then the magnitude of induced emf w ill be maximum and minimum, respectively at :

JEE MainJEE Main 2020Electromagnetic Induction

Solution:

Flux $\phi = \vec{B}\cdot \vec{A} = BA \,cos\,{}^{\theta\, BA \,cos\,\omega t}$
$|Induced\, emf| = |e| =\left|\frac{d\phi}{dt}\right| = \left|BA\omega\,sin\,\omega t\right|$
$|e|$ will be maximum at $\omega t = \frac{\pi}{2}$
$\left(\frac{2\pi}{T}\right)t = \frac{\pi }{2}$
$\left(\frac{2\pi }{10}\right)t = \frac{\pi }{2} \Rightarrow t = 2.5\,sec$
$|e|$ will be minimum at $\omega t = \pi$
$\left(\frac{2\pi }{10}\right)t = \pi \Rightarrow t = 5\,sec$