Question

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

Answer 1

Explanation:

this is the answer. a torque is acting which results in rotation

Answer 2

$\tau=PEsinx=\vec{P}\times \vec{E}$

Explanation:

Let two charges +q and -q are placed in uniform electric field E  and the distance between two charges =2l.

Force due to positive charge=qE

Force due to negative charge==-qE  

Two forces act in opposite direction.

Therefore, there is a couple of force which is called torque.

Torque=$F\times perpendicular\;distance$

In triangle  ABC

$sinx=\frac{BC}{2l}$

$BC=2lsinx$

Force, F=qE

Substitute the values then we get

$\tau=qE(2lsinx)$

$\tau=2lqEsinx$

P=2lq

Substitute the values

$\tau=PEsinx=\vec{P}\times \vec{E}$

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