Question

If the plates of a parallel plate charged capacitor are not parallel, the interface charge density is
A. Is higher at the closer end
B. In non-uniform
C. Is higher at inclined plate
D. Is uniform

Answer 1

Hint: For metallic plate capacitors, the potential is the same at each point on the plates. As it’s an equipotential surface. The charge density depends on the charge. And charge is inversely proportional to the distance between the plates.

Complete step by step answer:
The interface charge density depends on the charge of the capacitor. When there will be more charge in the capacitor the interface charge density will be more. And if the charge is relatively less than the charge density will be relatively less.
Now, the charge stored in a capacitor is given as follow:
$Q = CV$
Where $Q$ is the charge stored in the capacitor
$C$ is the capacitance and $V$ is the potential
Now as we have discussed earlier that the surfaces will be equipotential, now
And we know that $C = \dfrac{{A\varepsilon }}{d}$ where $A$ is the area of the cross section and $d$ is the distance between the plates. $\varepsilon $ is a constant.
$ \Rightarrow Q = \dfrac{{A\varepsilon V}}{d}$
From this equation, it is clear that the charge is inversely proportional to the distance between the plates. So, for parallel plates, the charge is constant and for plates which are not parallel, the charge will vary for different points as follows:
As distance is inversely proportional, this implies that when plates are closer the charge will be more. Hence the charge density will be large.
Therefore, option A and option C are correct.
And for plates which are farther away, the value of distance will be larger and hence the charge density will be lower.
It is clear from the above discussion that charge density is not uniform. Hence option B is also correct.

Therefore, option A, B and C are correct.

Note:
The magnitude of interface charge density depends inversely to the distance between the plates. When plates are closer, the charge density is highest and when the plates are far away from each other, the charge density gets lower. If plates are parallel the charge density will be uniform.