Question

Write the expression for work done in turning a dipole of dipole moment p from its position of stable equilibrium to a position of unstable equilibrium in a uniform electric field E .
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Answer 1

Solution :

⏭ Given:

✏ A dipole is placed in uniform electric field of magnitude E

⏭ To Find:

✏ Work requires to turn dipole of dipole moment P from its position of stable equilibrium to a position of unstable equilibrium.

⏭ Concept:

✏ For stable equilibrium, Angle between dipole moment and electric field = 0°

✏ For unstable equilibrium, Angle between dipole moment and electric field = 180°

⏭ Formula:

✏ Work requires to turn dipole from angle $\theta_1$ to $\theta_2$ is given by...

$\bigstar\: \boxed{\sf{\pink{W = PE(\cos\theta_1 - \cos\theta_2)}}}$

⏭ Calculation:

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$\circ\sf \: W = PE(\cos0\degree - \cos180\degree)\\ \\ \circ\sf \: W = PE[1-(-1)]\\ \\ \circ\: \boxed{\purple{\sf{\large{W = 2PE}}}}$

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✒ Work done to turn dipole from 0° to 180° = 2PE

Answer 2

$\black\huge{Answer}}}$

The condition of stable equilibrium is achieved when the direction of extrernal electric field is parallel to the direction of the dipole moment.

Hence, Potential Energy = -PEcos?

Since ?=0, cos ?=1

Thereferoe, potential energy=PE=maximum

In unstable equilibirum, the direction of the electric field is antiparallel to the direction of dipole moment.

therefore, ?=180 degrees. cos?= -1

hence, Potential enegy = -PE

Hence, total work done = Initial energy - final energy = PE - (-PE) = 2PE