A,B,C,D are four 'thin', similar metatllic parallel plates, equally separated by distanace d, and connected to a cell of p.d. (V), as shown in Fig.

(i) write the potentials of A,B,C and D.
(ii) If B and C be connected by a wire, then what will b e the potentials of the paltes ? (iii) How will the electric fields ? (iv) Will the charges on the plates A and D change ?

Explanation

(i) The potential of A is V and potential fo D (earthed) is zero. Since the plates are equidistant, the potentials of B and C are `2V//3 and V//3` respectively.
(ii) On connecting B and C, they will come to the same potential, each `= (1)/(2) ((2V)/(3) + (V)/(3)) = (V)/(2)` , A and
D will still remain at V and zero potential respecitively.
(iii) The electric field between A and B will increase from `V//3d` to `V//2d`, become zero between B and C, and increase from `V//3d to V//2d` between C and D.
(iv) The capacitance of the system was initially `in_(0) a//3d`, where a is area fo each plate. Now it has increased to `in_(0) a//2d`. Hence charges on A and D will increase.