Suppose there is a uniform electric field in the (+x)direction. If a negative charge moves in the (-x)direction; does the electric potential energy increase or decrease? Explain.

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Solution

$T h e e l e c t r i c p o t e n t i a l e n e r g y w i l l i n c e a s e b e c a u s e o f f o l l o w i n g r e a s o n, E l e l c t r i c p o t e n t i a l e n e r g y = - \int e E . d r = - \frac{1}{4 π ε_{0}} \times e \times \int_{r_{A}}^{r_{B}} \frac{q}{r^{2}} . d r W h e r e e i s e l e c t r o n i c c h a r g e, q t h e c h a r g e o f e l e c t r i c f i e l d E a n d r_{B} < r_{A} . O n i n t e g r a t i o n p o t e n t i a l e n e r g y b e c o m e s, U = - \frac{e q}{4 π ε_{0}} \times {[\frac{- 1}{r}]}_{r_{A}}^{r_{B}} = \frac{e q}{4 π ε_{0}} \times (\frac{1}{r_{B}} - \frac{1}{r_{A}}) . S i n c e r_{A} > r_{B}, t h e r e f o r e e l e c t r i c p o t e n t i a l e n e r g y i s p o s i t i v e .$

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