A medium having dielectric constant K 1 fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is d . The capacitor is connected

Question

A medium having dielectric constant K > 1 fills the space between the plates of a parallel plate capacitor. The plates have large area, and the distance between them is d . The capacitor is connected to a battery of voltage V . as shown in Figure (a). Now, both the plates are moved by a distance of d 2 from their original positions, as shown in Figure (b). In the process of going from the configuration depicted in Figure (a) to that in Figure (b), which of the following statement(s) is(are) correct?

TestHub · Accepted Answer

Capacitance of both capacitors are C a = K ε 0 A d and C b = ε 0 A d + d K = ε 0 A K d K + 1 Now, charge stored is q a = K ε 0 A d V and q b = ε 0 A K V d K + 1 . Electric field between each parallel plate capacitor is E a = q a K A ε 0 = K ε 0 A V d K ε 0 A = V d and E b dielectric = E air K = q b K A ε 0 = ε 0 A K V d K + 1 K A ε 0 = V d K + 1 So, from above relations, we can see that capacitance decrease by a factor of 1 K + 1 . Work done in the process W = U f - U i = 1 2 C f - C i V 2 = 1 2 ε 0 A K d K + 1 - K ε 0 A d V 2 = 1 2 V 2 ε 0 A K d 1 K + 1 - 1 = 1 2 ε 0 A K V 2 d 1 - K - 1 K + 1 = 1 2 ε 0 A V 2 d - K 2 K + 1 Thus, the work done in the process depends upon the dielectric material.

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