Two charged spheres attract each other they are made to touch each other and then placed at the same distance will be know attract or repel each other explain

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Solution

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Since the two spheres are attract each other its means both have opposite charges. Let the spheres have radius r and R having charges +q₁ and -q₂ respectively.
$W h e n t h e s p h e r e s t o u c h e a c h o t h e r c h a r g e s f l o w t i l l t h e b o t h s p h e r e s a q u i r e t h e s a m e p o t e n t i a l g i v e n b y V = \frac{q_{1} - q_{2}}{C_{1} + C_{2}} w h e r e C_{1} a n d C_{2} a r e t h e c a p a c i \tan c e s o f b o t h s p h e r e s g i v e n b y C_{1} = 4 π ε_{o} r a n d C_{2} = 4 π ε_{o} R V = \frac{q_{1} - q_{2}}{4 π ε_{o} (r + R)} a n d t h e n c h a r g e s o n s p h e r e s w i l l b e q_{1}' = C_{1} V a n d q_{2}' = C_{2} V l e t r = R t h e n V = \frac{q_{1} - q_{2}}{8 π ε_{o} r} V \propto (q_{1} - q_{2}) c a s e I i f q_{1} = q_{2} \Rightarrow V = 0 \Rightarrow q_{1}' = 0 a n d q_{2}' = 0 s p h e r e s n e i t h e r a t t r a c t n o r r e p e l . c a s e I I q_{1} > q_{2} o r q_{1} < q_{2} \Rightarrow V = + i v e o r V = - i v e r e s p e c t i v e l y \Rightarrow q_{1}' = + i v e a n d q_{2}' = + i v e o r q_{1}' = - i v e a n d q_{2}' = - i v e b o t h s p h e r e s w i l l r e p e l e a c h o t h e r .$

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Two like magnetic poles :

(a) repel each other

(b) attract each other

(d) neither attract nor repel.

Why do like charges repel each other? Why do not they attract each other ?

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