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# Dipole Potential Energy Assignment Help

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Electrostatics - Dipole Potential Energy

Dipole Potential Energy

Potential energy of dipole is the energy possessed by the dipole by virtue of its particular position in the electric field.

Suppose an electric dipole of moment ~P is oriented at a **∠ θ** with the direction of uniform external electric field ~E. We know that, the torque ~ζ acting on the dipole is

**ζ = p E sin θ**

It tries to rotate the dipole.

Small amount of work done in rotating the dipole through a small angle d θ against the torque is

**dW = ζ d θ **

**= p E sin θ d θ**

∴ Total work done in rotating the dipole from orientation **θ**_{1} to **θ**_{2} is

**W =**_{θ1}∫^{θ2} E sin θ d θ

= p E [- cos θ]_{θ1}^{θ2}

**W = - p E [cos θ2 – cos θ1] (1)**

**P.E. = W = - pE (cos θ2 – cos θ1) (2)**

Particular cases:

When the dipole is initially aligned along the electric field i.e. **θ1 = 0°,** and we have to set it angle θ with ~Ei.e. **θ**_{2} = θ.

**From (2), W = - pE (cos θ – cos 0°)**

W = - pE (cos θ – 1) (3)

This work done is stored in the dipole in the form of potential energy.

When the dipole is initially at right angle to ~E i.e.** θ**_{1} = 90°, and we have to set it at angle θ with ~E i.e.**θ**_{2} = θ.

**∴** From (2), **W = - pE (cos θ – cos 90°)**

**W = - pE cos θ**

∴ Potential energy of dipole,

**U = W = - pE cos θ (4)**

**U = - ~P.~E (5)**

Obviously, potential energy of an electric dipole is a scalar quantity. It is measured in joule.

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Suppose an electric dipole of moment ~P is oriented at a

**∠ θ**with the direction of uniform external electric field ~E. We know that, the torque ~ζ acting on the dipole is

**ζ = p E sin θ**

It tries to rotate the dipole.

Small amount of work done in rotating the dipole through a small angle d θ against the torque is

**dW = ζ d θ**

**= p E sin θ d θ**

∴ Total work done in rotating the dipole from orientation

**θ**

_{1}to

**θ**

_{2}is

**W =**

_{θ1}∫

^{θ2}E sin θ d θ

= p E [- cos θ]

_{θ1}

^{θ2}

**W = - p E [cos θ2 – cos θ1] (1)**

**P.E. = W = - pE (cos θ2 – cos θ1) (2)**

Particular cases:

When the dipole is initially aligned along the electric field i.e.

**θ1 = 0°,**and we have to set it angle θ with ~Ei.e.

**θ**.

_{2}= θ**From (2), W = - pE (cos θ – cos 0°)**

W = - pE (cos θ – 1) (3)

W = - pE (cos θ – 1) (3)

This work done is stored in the dipole in the form of potential energy.

When the dipole is initially at right angle to ~E i.e.

**θ**, and we have to set it at angle θ with ~E i.e.

_{1}= 90°**θ**.

_{2}= θ**∴**From (2),

**W = - pE (cos θ – cos 90°)**

**W = - pE cos θ**

∴ Potential energy of dipole,

**U = W = - pE cos θ (4)**

**U = - ~P.~E (5)**

Obviously, potential energy of an electric dipole is a scalar quantity. It is measured in joule.