Question

A highly conducting ring of radius $R$ is perpendicular to and concentric with the axis of a long solenoid as shown in figure. The ring has a narrow gap f width $\delta$ in its circumference. The cross-sectional area of the solenoid is $a$. The solenoid has a uniform internal field of magnitude $B\left(t\right)=B_0+\beta t$, where $\beta >0$. Assume that no charge can flow across the gap, the face(s) accumulating an excess of positive charge is/are

• A. $F_1$
• B. $F_2$
• C. $F_1$ and $F_2$
• D. difficult to conclude as data given are insufficient
• E. answer required

Answer 1

The correct option is A $F_1$

According to Lenz law, change in flux passing through a conducting coil induces an emf (OR current) in the coil in such a way that it opposes the change in the flux.

Now magnet field in the solenoid is given as $B\left(t\right)=B_o+\beta t$ where $\beta >0$

$⟹B\left(t\right)$ will go on increasing with time, hence the flux through the conducting ring will also increase inducing a current $I$ in anticlockwise direction so that it opposes the change in flux.

$\therefore$ Electrons flow in clockwise direction whereas the holes flow in anticlockwise direction.

But as the charge cannot flow through the gap, thus these charges get accumulated at the faces making the face $F_1$ as of positive charge whereas face $F_2$ as of negative charge.