Question

Three large non conducting plates $P,Q$ and $R$ having uniform charge densities $\sigma ,\sigma$ and $-\sigma$ are placed parallel to each other. A ring of area $S$ parallel to plate area is placed between the plates $Q$ are $R$ as shown.
The electric flux through the ring is

• A. $\frac{3\sigma S}{{\epsilon }_0}$
• B. $\frac{2\sigma S}{{\epsilon }_0}$
• C. $\frac{\sigma S}{{\epsilon }_0}$
• D. $\frac{3\sigma S}{2{\epsilon }_0}$

Answer 1

The correct option is A $\frac{3\sigma S}{{\epsilon }_0}$

For plate PQR only right side electric field produce

For plate R there is repetitive shape Q it

So, left side will add flux

$E_{net}=\left(\frac{\sigma }{{\epsilon }_0}+\frac{\sigma }{{\epsilon }_0}+\frac{\sigma }{{\epsilon }_0}\right)$

$Q=\left({\epsilon }_{net}\times A\right)=\frac{3\sigma }{\epsilon }A$