what orientation of an electric dipole in a uniform electric field corresponds to its a) stable b) unstable equilibrium ?

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Solution

$P o t e n t i a l e n e r g y o f d i p o l e i n u n i f o r m e l e c t r i c f i e l d i s g i v e n b y : U = - \vec{P} . \vec{E} U = - P E \cos θ w h e r e θ i s t h e a n g l e b e t w e e n d i p o l e m o m e n t a n d e l e c t r i c f i e l d . w h e n θ = 0 U = - P E h e n c e p o t e n t i a l e n e r g y i s m i n i m u m t h e r e f o r e i t i s t h e s t a b l e c o n f i g u r a t i o n . w h e n θ = 180^{o} U = - P E \cos 180 U = P E p o t e n t i a l e n e r g y i s m a x i m u m h e n c e t h i s i s u n s t a b l e c o n f i g u r a t i o n .$

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