Question

A flat coil, $C$ of $n$ turn, area $A$ and resistance $R$, is placed in a uniform magnetic field of magnitude $B$. The plane of the coil is initially perpendicular to $B$. The coil is rotated by an angle $\theta$ about a diameter and charge of amount $Q$ flows through it. If the coil rotates with a constant angular velocity $\omega$, the emf induced in it:

• A. is zero
• B. changes non-linearly with time
• C. has a constant value$=BAn\omega$
• D. has a maximum value $=BAn\omega$
• E. answer required

Answer 1

Answer: (B), (D)

changes non-linearly with time
has a maximum value $=BAn\omega$

$\varphi =nB.A=BnAcos\left(\theta \right)=BAncos\left(\omega t\right)$
$E=\frac{d\varphi }{dt}=BAn\omega sin\left(\omega t\right)$
It has a sinusoidal behavior
$E_{max}=BAN\omega$, when $\omega t=n\pi$