Define capacitance of capacitor. Write its S.I. Unit. Derive expression for capacitance of parallel plate capacitor when medium between plates is air.

**OR**

Establish an expression for the intensity of the electric field in equatorial position at a distance "x" from the midpoi

Question

Define capacitance of capacitor. Write its S.I. Unit. Derive expression for capacitance of parallel plate capacitor when medium between plates is air.

**OR**

Establish an expression for the intensity of the electric field in equatorial position at a distance "x" from the midpoint of an electric dipole and tell its direction.

Accepted Answer

>

> [!TLDR]
> $C=Q/V$ (farad); for parallel plates in air, using the uniform field $E=\sigma/\varepsilon_0$, we get $C=\varepsilon_0A/d$.
>
> **Definition:** The capacitance of a capacitor is the ratio of the charge $Q$ given to either plate (conductor) to the potential difference $V$ developed between them:
> $$C = \frac{Q}{V}$$
> **SI unit:** farad (F), where $1\ 	ext{F} = 1\ 	ext{C/V}$ (a very large unit in practice; common sub-units are $\mu F$, $nF$, $pF$).
>
> **Derivation — parallel plate capacitor with air (vacuum) between plates:**
>
> Consider two parallel conducting plates, each of area $A$, separated by a small distance $d$, carrying charges $+Q$ and $-Q$, with surface charge density $\sigma = Q/A$.
>
> The uniform electric field between the plates (from Gauss's law, for two oppositely charged infinite sheets):
> $$E = \frac{\sigma}{\varepsilon_0} = \frac{Q}{\varepsilon_0 A}$$
>
> Since the field is uniform, the potential difference between the plates: …

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