Name: Equipotential Surfaces and Its Properties
Uploaded: 2019-07-19
Duration: 7 min 22 s
Description: The surface over which the electric potential is the same everywhere is called an equipotential surface. Let's more about it and its properties in this video.

Question

Define electric potential. Obtain an expression of electric potential due to an electric dipole at any point

(r, θ)

. Draw necessary diagram.

Accepted Answer

The electric potential at a point is equal to the work done by external force in bringing the unit positive charge from infinity to a point inside the electric field without changing the kinetic energy.

Let an electric dipole consist of two equal and opposite point charges –q at A and +q at B ,separated by a small distance AB =2a ,with centre at O.

The dipole moment, p=q×2a

We will calculate potential at any point P, where

OP=r and $∠ B O P = θ$

Let $B P = r_{1} a n d A P = r_{2}$

Draw AC perpendicular PQ and BD perpendicular PO

$I n △ A O C, \cos θ = O C / O A = \frac{O C}{a} O C = a \cos θ O D = a \cos θ$

Potential at P due to +q $= \frac{1}{4 {πε}_{0}} \frac{q}{r 2}$

And Potential at P due to −q= $\frac{1}{4 {πε}_{0}} \frac{q}{r 1}$

Net potential at P due to the dipole

$V = \frac{1}{4 {πε}_{0}} [\frac{q}{r_{2}} - \frac{q}{r_{1}}]$

Now, r1 =AP=CP

=OP+OC

$= r + a \cos θ$

And r2 =BP=DP

=OP–OD

$= r - a \cos θ$

$V = \frac{q}{4 {πε}_{0}} (\frac{1}{r - a \cos θ}) - (\frac{1}{r + a \cos θ}) = \frac{q}{4 {πε}_{0}} (\frac{2 a \cos θ}{r^{2} - a^{2} \cos^{2} θ}) = \frac{p \cos θ}{r^{2} - a^{2} \cos^{2} θ}$

Define electric potential. Obtain an expression of electric potential due to an electric dipole at any point $(r, θ)$ . Draw necessary diagram.

Important Questions on Electrostatic Potential and Capacitance

Learn and Prepare for any exam you want !

Define electric potential. Obtain an expression of electric potential due to an electric dipole at any point r, θ. Draw necessary diagram.

Important Questions on Electrostatic Potential and Capacitance

Learn and Prepare for any exam you want !

Define electric potential. Obtain an expression of electric potential due to an electric dipole at any point $(r, θ)$ . Draw necessary diagram.