Question

A coil is rotated with constant angular speed in a uniform magnetic field about an axis that is perpendicular to the field.

$\text{STATEMENT-1}:$ The EMF induced in the coil is maximum at the instant the magnetic flux through the coil is zero.

$\text{STATEMENT-2}:$ The angle between the normal to the coil and magnetic field induction is ${90}^{\circ }$.

• A. Both $\text{STATEMENT-1}$ and $\text{STATEMENT-2}$ are $\text{WRONG}$
• B. Both $\text{STATEMENT-1}$ and $\text{STATEMENT-2}$ are $\text{TRUE}$ but $\text{STATEMENT-2}$ is the $\text{NOT}$ the correct explanation of $\text{STATEMENT-1}$
• C. Both $\text{STATEMENT-1}$ and $\text{STATEMENT-2}$ are $\text{TRUE}$ and $\text{STATEMENT-2}$ is the correct explanation of $\text{STATEMENT-1}$
• D. $\text{STATEMENT-1}$ is $\text{FALSE}$ and $\text{STATEMENT-2}$ is $\text{TRUE}$

Answer 1

The correct option is C Both $\text{STATEMENT-1}$ and $\text{STATEMENT-2}$ are $\text{TRUE}$ and $\text{STATEMENT-2}$ is the correct explanation of $\text{STATEMENT-1}$

Let the angle between the normal to the coil and magnetic field induction be $\theta$.

We know that, $\varphi =BA\cos \theta$

Differentiating on both sides wrt $\left(t\right)$ gives,

$-\frac{d\varphi }{dt}=BA\sin .\frac{d\theta }{dt}$

From Lenz's law, $E_{in}=BA\omega \sin \theta [\frac{d\theta }{dt}=\omega ]$

$\therefore E_{in}$ is maximum when, $\theta ={90}^{\circ }$

Flux $\varphi =0$ at this instant.