Question

A straight conducting rod $PQ$ is executing $\text{SHM}$ in $xy-$plane from $x=-d$ to $x=+d$. Its mean position is $x=0$ and its length is along $y-$ axis. There exists a uniform magnetic field $B$ from $x=-d$ to $x=0$ pointing inward normal to the paper and from $x=0$ to $=+d$ there exists another uniform magnetic field of same magnitude $B$ but pointing outward normal to the plane of the paper. At the instant $t=0$, the rod is at $x=0$ and moving to the right. The induced emf $\left(\epsilon \right)$ across the rod $PQ$ vs time $\left(t\right)$ graph will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

At mean position, velocity is maximum. Hence motional emf $|Bvl|$ is also maximum. $v$ oscilIates simple harmonically. Hence, motional emf will also be sinusoidal. Further, polarity of induced emf will keep on changing.