Question

Defind the terms (i) capacitance of a capacitor
(ii) strength of dielectric placed between the plates of a charged parallel plate capacitor, fully occupying the intervening region.
iii)How does the polarisation of the dielectric medium effect the net electric field?
iv) For linear dielectrics show that the introduction of dielectric increases its capacitance by a factor of a characteristic of the dielectric.

Solution

i) Capacitance of a capacitor is defined as the ratio of the electric charge on the capacitor to the electric potential of capacitor due to it's charge.

ii) Dielectric strength of a dielectric is defined as the maximum value of electric field that can be applied to the dielectric without it's electric breakdown.
The unit of dielectric strength is Volt per metre.

iii) When a dielectric slab is introduced in between the plates of capacitor, the electric field gets reduced.
Consider a parallel plate capacitor with vaccum in between it's plates. The capacitor is charged up with battery such that electric field is set up between it's plates.

Then, $E_{\circ} = \frac{σ}{ε_{\circ}}$

where, $σ$ is the surface charge density of the plates.
Now, as soon as the dielectric is introduced in between the plates each molecule of the dielectric get's polarised. Charges are induced on the surface of the dielectric and, these induced charges set up an electric field E_P inside the dielectric.
Therefore, the resultant electric field gets reduced and is given as
E=E_o- E_P

iv) When there is vaccum in between the plates, capacitance is given by C= $\frac{ε_{\circ} A}{d}$ .

When, dielctric is inserted in between the plates, Capacitance increases by a factor of K.
where, K is the dielectric constant.

Capacitance becomes C= $K \frac{ε_{\circ} A}{d}$ .

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