Question

A dipole of dipole moment is rotated inside a uniform electric field from its stable equilibrium position to unstable equilibrium position slowly. Then work done by external agent is?

Answer 1

Answer:

 stable equilibrium the angle between p and E , θ₁ = 0° 

For unstable equilibrium,θ₂ = 180° 

Work done in rotating the dipole from angle θ₁ to θ₂ 

W = pE(cosθ₁-cosθ₂) = pE(cos0°-cos180°)

= 2pE.

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Answer 2

Answer:

Work done by external agent = 2PE

A pair of force which is equal in magnitude with opposite direction , and displaced by perpendicular distance or moment is known as a couple.

For an electric dipole p in a uniform field E we write the work done by external agent in rotating dipole as dW= pEcosθ dθ

Step by step explanation :

If the dipole is rotated from an angle θ$_{1}$ to θ${2}$

then work done by external force is given by

       W = pE [cos θ$_{1}$ - cos θ${2}$ ]

For stable equilibrium the angle between  p and E , θ$_{1}$ =0°

For unstable equilibrium θ$_{2}$ =180°

work done in rotating the dipole from θ$_{1}$ to θ$_{2}$

W =pE (cos θ$_{1}$ - cos θ$_{2}$ )

 = pE ( cos 0° - cos 180° )

    = pE ( 1 - ( -1))

   = 2pE

From the above we conclude that work done by external agent =

        2pE.

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