Question

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 $10s$ about an axis in its plane then the magnitude of induced emf w ill be maximum and minimum, respectively at :

• A. $2.5s$ and $7.5s$
• B. $5.0s$ and $7.5s$
• C. $5.0s$ and $10.0s$
• D. $2.5s$ and $5.0s$

Answer 1

Answer: (D)

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