Question

There identical metal plates with large surface areas are kept parallel to each other as shown in figure (30-E8). The leftmost plate is given a charge Q.the rightmost a charge -2Q and the middle one remains neutral. Find the charge appearing on the outer surface of the rightmost plate.

Answer 1

(a) For the surface charge density of a single plate. Let surface charge density at both side be ${\sigma }_1$ and ${\sigma }_2$

Now electric field at both ends

$=\frac{{\sigma }_1}{2{\in }_0}and\frac{{\sigma }_2}{2{\in }_0}$

Due to net balanced electric field on plate and $r_1$ equal to $r_2$

$q_1=q_2=\frac{Q}{2}$

Net surface charge density =$\frac{Q}{2A}$

(b) Electric field to the left of the plates since

$r=\frac{Q}{2A}$

Hence,electric field =$\frac{Q}{2A{\in }_0}$

This must be directed towards left 'X' is the charge plate.

(c) and (d) here in both the cases the charged plate 'X' acts as the only source of electric field, with +ve in the inner side and 'Y' attracts towards it with -ve in its innerside. So for the middle portion E is towards right.

(d) Similarly for extreme right the outer side of the 'Y' plate acts as +ve and hence

it repels to the right with $E=\frac{Q}{2A{\in }_0}$