Name: Dielectrics in a Capacitor
Uploaded: 2019-07-19
Duration: 6 min 3 s
Description: Let us use our knowledge about dielectrics and capacitors to find out how the use of dielectrics can increase the capacitance of a system. Learn through this...

Question

Two conducting plates $X$ and $Y$ , each having large surface area $A$ (on one side), are placed parallel to each other as shown in figure. The plate $X$ is given a charge $Q$ whereas the other is neutral. Find

(a) The surface charge density at the inner surface of the plate $X$ .

(b) The electric field at a point to the left of the plates,

(c) The electric field at a point in between the plates and

(d) The electric field at a point to the right of the plates.

Accepted Answer

$(a)$ Given the charge on the plate $X$ is $Q$ . Due to convection ,other plate $Y$ will get the same charge.Suppose the surface charge densities on both sides of the plates be $σ_{1}, σ_{2}$ respectively.There magnitude of the electric fields due to plates on each side will be $\frac{σ_{1}}{2 \in_{\circ}}$ and $\frac{σ_{2}}{2 \in_{\circ}}$

Also note that the plate has two sides each of same area $A$ . So the net charge $Q$ given to the plate will be distributed equally on both the sides.This implies charge developed on each side will be given by, $q_{1} = q_{2} = \frac{Q}{2}$

Therefore surface charge density on each side will be charge per unit area that is $\frac{Q}{2 A} .$

$(b)$ Now electric field to the left of plates $= \frac{σ}{\in_{\circ}}$ ,since $σ = \frac{Q}{2 A}$ , hence electric field $= \frac{Q}{2 A \in_{\circ}}$

Since $X$ is positively charged plate, this field must be directed to left.

$(c)$ Please note, here the charged plate $X$ acts as the only source of electric field, with positive on inner side.Plate $Y$ is neutral. Hence a negative charge will be induced on its inner side.Hence there is attraction towards $Y$ . SO electric field in between the plates is directed towards right is equal to $\frac{Q}{2 A \in_{\circ}}$ .

$(d)$ Similarly, for the extreme right, the outer side of the plate $X$ acts as positive ,hence it repels to the right with $Y$ .

Important Questions on Capacitance

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