Question

Three identical metal plates with large surface areas are kept parallel to each other as shown in figure. The leftmost plate is given a charge Q, the rightmost a charge $-2Q$ and the middle one remain neutral. The charge appearing on the outer surface of the rightmost plate is?

• A. $\frac{Q}{2}$
• B. $\frac{Q}{3}$
• C. $-\frac{Q}{2}$
• D. $-\frac{Q}{4}$

Answer 1

The correct option is C $-\frac{Q}{2}$

by applying gauss law

the metal field is zero

electric field at the point p

E $\frac{Q-q}{2\pi {\epsilon }_o}+\frac{q}{2\pi {\epsilon }_o}-\frac{q}{2\pi {\epsilon }_o}+\frac{q}{2\pi {\epsilon }_o}+\frac{2Q+q}{2\pi {\epsilon }_o}=0$

$q=\frac{-3Q}{2}$

change appearing

$-2Q-q=-2q+\frac{3Q}{2}$

$-\frac{Q}{2}$