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

Derive the expression for a couple acting on an electric dipole in a uniform electric field.

Accepted Answer

Consider an electric dipole having charges $- q$ and $+ q$ and the distance between them is $2 a$ . It is placed in a uniform electric field $E$ making an angle $θ$ with the direction of the field.

We know the electric field due to the force $F$ experienced by a charge is:

$\vec{E} = \frac{\vec{F}}{q}$

$∴ \vec{F} = q \vec{E}$

Force on charge $+ q$ ,

$\vec{F} = + q \vec{E}$

Also, the force on charge $- q$ ,

$\vec{F} = - q \vec{E}$

The net force acting on a dipole in the uniform electric field is zero.

But these two equal and opposite forces generate torque or a moment of couple on the dipole.

We know that,

$τ = F d$ where $F$ is the magnitude of either force and $d$ is the perpendicular distance between the two forces.

$τ = (q E) (2 a \sin θ)$

$τ = (2 q a) (E \sin θ)$

$τ = P E \sin θ$

Here, $P$ is the dipole moment.

Therefore, the couple acting on electric dipole is $τ = P E \sin θ$ .

Derive the expression for a couple acting on an electric dipole in a uniform electric field.

Important Questions on Electric Charges and Fields

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