Answer to Question #189308 in Electricity and Magnetism for Aqsa

Question

What will happen to the dipole when it place inside the

uniform Electric Field

NOTE:. Your Assignment should cover following points

• What is a dipole

• what is force acting on dipole

• what is torque on dipole

• expression for potential energy of d

ipole

Answer 1

Dipole:-

The product of magnitude of negative or positive charge(q) and the distance between the centres of the positive and negative charges is called dipole

$p=|q|d$

Unit $=C\times m$

(b)

An electric dipole experiences a net electric force if the positive charge q is subject to an electric field E (r + d) that differs from E(r) acting on the negative charge q.

At d distance force

$F=qE$

At d+∆d distance force

$F=q[E(r+d)-Er]$

$F_{x}=q[E_{x}(x+dx,y+dy,z+dz)-E_{x}(x,y,z)]$

We can express this equation

$$F_{x}=q[E_{x,}(x,y,z)+d_{x}\frac{\partial {E_{x}}}{\partial x}+d_{y}\frac{\partial {E_{y}}}{\partial y}+d_{z}\frac{\partial {E_{z}}}{\partial z}+............................. -E_{x,}(x,y,z)]$$

First and last term cancel

Then we can written as

$F_{x}=p.\nabla E_{x}$

y components

$F_{y}=p.\nabla E_{y}$

z components

$F_{z}=p.\nabla E_{z}$

Summarized in vector expression

$F=p.\nabla E \rightarrow(1)$

(c) torque of dipole

$\overrightarrow{\tau}=\overrightarrow{p}\times\overrightarrow{E}$

$\tau=pEsin\theta$

Where P =qd

(d) Potential energy

$U=-\overrightarrow{p}.\overrightarrow{E}$

$U=-pEcos\theta$