four equal charge are placed at corners of square of side a. show that charge placed at centre of sqaure will be in equilibrium ?

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Solution

$S i n c e a c h a r g e i s p l a c e d a t t h e c e n t r e o f a s q u a r e h a v i n g f o u r e q u a l c h a r g e s a t i t s f o u r c o r n e r s . T h e c h a r g e a t t h e c e n t r e o f t h e s q u a r e i s r e p e l l e d b y e q u a l m a g n i t u d e a c r o s s t h e d i a g o n a l o f t h e s q u a r e w h i c h a r e i n o p p o s i t e d i r e c t i o n s . S o t h e s e f o r c e s w i l l c a n c e l o u t a n d t h e c h a r g e a t t h e c e n t r e o f t h e s q u a r e i s i n e q u i l i b r i u m a s n o f o r c e i s a c t i n g o n i t .$

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