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Derive an expression for potential energy of electric-dipole placed in an uniform electric field. |
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Answer» Solution :We know that torque on an electric dipole placed in an electric field, `tau=pE SIN theta` By DEFINITION work done by torque on the dipole `dW=tau d theta` i.e., `dW=pEsin theta .d theta` Net work done to move from`theta_1` to `theta_2` is GIVEN by `W=int dW=int_(theta_1)^(theta_2) pE sin theta d theta` i.e.,`W=-pE (cos theta )_(theta_1)^(theta_2)` i.e., `W=-pE (cos theta_2 - cos theta_1)` Taking `theta_1=90^@` and `theta_2=theta` ,we can write , `W=-pE cos theta ` or `W=-vecp.vecE` . This work done will be storedin the form of potential energy . i.e.,`P.E.=-vecp.vecE` |
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