Question

The parallel plates of an isolated capacitor carry opposite charges, Q. If the separation of the plates is increased, is a force required to do so? Is the potential difference changed? What happens to the work done in the pulling process?

Short answer

A force is required to separate the plates. The potential difference is also increased with the increase in charge. The work done will increase in the pulling process.

Step-by-step solution

Relationship between the Coulomb force, the magnitude of the charges and separation between the charges

The value of Coulomb’s force between the charged particles is directly related to the product of charges and inversely related to the square of the separation between the charges.

Application of Coulomb force

The plates of the capacitor have opposite charges. So, there is a force of attraction between the plates of the capacitor. To increase the separation between the plates of an isolated capacitor having opposite charges, a force similar to the force of attraction between the charges is required.

Therefore, a force is required to increase the separation between the plates.

Relationship between the potential difference and the separation between the plates

The charge on the plate of the capacitor is related to the potential difference by the following equation:

\(V = \left( {\frac{Q}{{A{\varepsilon _o}}}} \right)d\)

Here, \(Q\) is the charge, \(A\) is the sectional area, \({\varepsilon _{\rm{o}}}\) is the permittivity of free space, and \(d\) is the separation between the charges.

From the above equation, it is clear that the potential difference is directly related to the separation between the charges.

Thus, the potential difference is also increased with the increase in separation.

Relationship between the work done and potential difference

The work done in pulling the plates apart is related to the charge and potential difference across the plates. That is,

\(W = Q\Delta V\)

From the above equation, it is clear that the value of the work done is directly related to the potential difference. So, the work done by pulling the plates is increasing with the increase in potential difference.

Thus, work done is increasing.