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Derive an expression for electric potential energy of a systemm of charges in an electric field. |
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Answer» <P> Solution :CONSIDER an electric dipole in an uniform electric FIELD `vec(E)` with its dipole moment `vec(p)` making an angle `theta` with the field as shown in fig.The torque acting on the dipole is `tau = pE sin theta` ………(1) If the dipole is rotated through a small angle `d theta` against the torque acting on it, the small amount og work DONE during this process is `d W = tau d theta` .......(2) From (1) `dW = p E sin theta d theta` .........(3) `therefore` The total amount of work done in rotating the dipole from its orientation `theta_(1)` to `theta_(2)` is `W = underset(pi//2)overset(theta)int pE sin theta` `= pE [-cos theta]_(pi//2)^(theta)` `= pE[-cos theta - cos""(pi)/(2)] "" | therefore cos""(pi)/(2) = 0` `W = -pE cos theta` ..........(3) This work done is stored as the ELECTROSTATIC potential energy of the dipole `therefore U = -pE cos theta` `U = -vec(p).vec(E)` 
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