Chapter 19: Q7 Q (page 794)

How does the final (equilibrium) charge on the capacitor plates depend on the size of the capacitor plates? On the spacing between the capacitor plates? On the presence of a plastic slab between the plates?

Short Answer

Expert verified

The final charge on the capacitor plates is directly proportional to the dielectric constant of the plastic slab and area of the plates and inversely proportional to the separation distance between the plates of the capacitor.

Step by step solution

Write the given data from the question.

The plastic slab is placed inside the capacitor plates.

Determine the formulas to find out, how the final charge depends on size of capacitor plates, spacing between plates and dielectric constant of slab.

The expression to calculate the capacitor when it is filled with the dielectric material is given as follows.

$c = \frac{E_{0} A A K}{d}$

Here, $A$ is the area of the plates, $K$ is the dielectric constant and $d$ is the separation between the plates.

The expression to calculate the charge on the plates is given as follows.

$Q = C △ V$ …… (i)

Here, $△ V$ is the potential difference between the plates of capacitor.

how the final charge depends on size of capacitor plates, spacing between plates and dielectric constant of slab.

Calculate the charge on the plates of the capacitors.

Substitute $\frac{E_{0} A K}{d}$ for $C$ into equation (i).

Q = \frac{E_{\circ} A K}{d} △ V

Q = (△ V E_{\circ}) \frac{A K}{d}

Let assume $△ V E_{\circ}$ is constant.

Q α \frac{A K}{d}

From the above equation, it is clear that the final charge on the capacitor plates is directly proportional to the dielectric constant of the plastic slab. The final charge increases with an increase in the area of capacitor plates and decreases with decreases in the area of plates. The final charge increases with an increase in dielectric constant and decreases with decreases in dielectric constant.

The final charge is inversely proportional to the separation distance between the capacitor plates. The value of the final charge increases with decreased separation distance and vice-versa.

Hence the final charge on the capacitor plates is directly proportional to the dielectric constant of the plastic slab and the area of the plates and inversely proportional to the separation distance between the plates of the capacitor.