Question

Three concentric spherical shells have radii r, 2r, and 3r. Innermost and outermost shells are earthed. Now charges on the shells are , and respectively. Then :

This question has multiple correct options
A

B

C

D

Hard
Solution
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Correct options are A) , B) and C)

At outside point at a distance from its centre, 
         
At inside point, it is constant, same as that over its surface,
         

     

Potential being a scalar quantity, it will be added due to all the spheres at a point.

So, Potential at sphere
               
                                  (For spheres & , sphere is a inside point, so using formula accordingly)

Potential at sphere
                
                                  (For spheres & , sphere is a outside point, so using formula accordingly)
               

On earthing potential becomes zero:

Therefore, from equation 
             

                        
 
Therefore, from equation 
             

                              

                           

On solving (3) and (4), we get:
              and

Hence, option are correct.

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