Name: Electric Field Produced by a Dipole
Uploaded: 2019-07-19
Duration: 32 min 17 s
Description: What is the electric field of a dipole? Watch the video to understand how the vector addition can be used to determine the electric field of a dipole.

Question

Establish the relationship between electric field intensity and electric potential.

Accepted Answer

To derive the relation, we will consider a positive point charge that produces an electric field $E$ at a point where a positive unit charge is placed.

We will attempt to move the unit charge by an infinitesimal distance $dx$ away from the point charge without any acceleration. Hence, an external force $F$ must be applied that is equal in magnitude and opposite in direction to the force due to the electric field.

Hence, the displacement and the external force are in opposite directions.

Work done $W$ by a force $F$ on a body is

$W = Fs . . . . . . . . (i)$

Where $s$ is the displacement of the body in the direction of the force. Using $(i)$ , we get, the work done $dW$ by the external force as

$dW = - Fdx . . . . . . . . (ii)$

The negative sign is because the external force and displacement are opposite in direction. The electric field $E$ due to a point charge at a point is the force $F$ per unit charge acting on a charged body of charge $q$ placed at that point.

$E = \frac{F}{q} . . . . . . . (iii)$

Hence, from the explanation above, since the charge at the point is a unit charge, putting this information in equation $(iii)$ , we will get,

$E = \frac{F}{1} = F . . . . . . . (iv)$

Putting $(iv)$ in $(ii)$ , we get,
$dW = - Edx . . . . . . . (v)$

The electric potential due to a point charge is the external work done to move a unit charge against the electric field by an infinitesimal distance without any acceleration. Using this definition, we get that the change in electric potential $dV$ due to the point charge will be

$dV = - Edx$ (From equation $(v)$ )

$∴ E = - \frac{dV}{dx}$

Hence, the electric field due to a point charge is the negative of the potential gradient due to the point charge.

Establish the relationship between electric field intensity and electric potential.

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