Saved Bookmarks
| 1. |
(a) Derive an expression for the potential energy of an electric dipole in a uniform electric field. Explain conditions for stab le and unstable equilibrium. (b) Is the electrostatic potential necessarily zero at a point where the electric field is zero ? Give an example to support your answer. |
|
Answer» Solution :(a) Let an electric, dipole of dipole moment `vecP` be PLACED in an electric FIELD `vecE` making an ANGLE `theta` with the direction of electric field intensity `vecE`. The torque acting on the dipole is given by : `vectau=vecPxxvecE` `tau=PE sin theta` work done to rotate the dipole through an angle `dtheta` `d omega=tau d theta= PE sin theta d theta` work done to rotate the dipole from `theta_(1)" to "theta_(2)` W=int_(theta_(1))^(theta_(2))PE sin theta d theta=PE[-cos theta]_(theta_(1))^(theta_(2))=-PE(cos theta_(2)-cos theta_(1))` `"If "theta_(1)=90^(@) and theta_(2)=theta""U=-PE cos theta =vecP.vecE` for stable equilibrium `theta=0^(@) rArr tau = 0 rArr U=-PE` for unstable equilibrium `theta=180^(@)rArr tau =0 rArr U = + PE.` (b) No. For EXAMPLE : Let we have TWO positive charges of same magnitude are placed at point A and B respectively. Electric field at mid pint O is zero but the electrostatic potential is `V=(1)/(4pi in_(0))(q)/(r)xx2` `V=(1)/(4pi in_(0))(2q)/(r).` 
|
|