Name: Dielectrics in a Capacitor
Uploaded: 2019-07-19
Duration: 6 min 3 s
Description: Let us use our knowledge about dielectrics and capacitors to find out how the use of dielectrics can increase the capacitance of a system. Learn through this...

Question

Derive an expression for electric potential due to a point charge. How do electric potential vary with distance

‘ r ’

for a point charge?

Accepted Answer

Let $+ q$ be an isolated point charge situated in air at $O$ . $P$ is a point at a distance $r$ from $+ q$ .

Consider two points $A$ and $B$ at distances $x$ and $x + d x$ from the point $O$ .

The potential difference between A and B is, $d v = - E d x$ .

The force experienced by a unit positive charge placed at A is

$E = \frac{1}{4 {πε}_{o}} \frac{q}{x^{2}} ∴ d V = \frac{1}{4 {πε}_{o}} \frac{q}{x^{2}} d x$

The negative sign indicates that the work is done against the electric force.

The electric potential at the point P due to the charge $+ q$ is the total work done in moving a unit positive charge from infinity to that point.

$V = - \int_{\infty}^{r} \frac{q}{4 {πε}_{o} x^{2}} d x = \frac{q}{4 {πε}_{o} r}$

For a point charge,

$V = \frac{1}{4 {πε}_{o}} (\frac{q}{r}) = > V a \frac{1}{r}$

The electric potential varies inversely with the distance.

Derive an expression for electric potential due to a point charge. How do electric potential vary with distance $‘ r ’$ for a point charge?

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Derive an expression for electric potential due to a point charge. How do electric potential vary with distance ‘r’ for a point charge?

Important Questions on Electrostatic Potential and Capacitance

Learn and Prepare for any exam you want !

Derive an expression for electric potential due to a point charge. How do electric potential vary with distance $‘ r ’$ for a point charge?