Question

A metal sphere is surrounded by an uncharged concentric thin spherical shell with a charge q and the potential difference between them is V. What is the new potential difference between them, if the shell is now given an additional charge q?

Answer 1

Answer:

As given in the first condition:

Both conducting spheres are shown.

V  

in

​  

−V  

out

​  

=(  

r  

1

​  

 

kQ

​  

)−(  

r  

2

​  

 

kQ

​  

)

=kQ(  

r  

1

​  

 

1

​  

−  

r  

2

​  

 

1

​  

)=V

In the second condition:

Shell is now given charge −4Q.

V  

in

​  

−V  

out

​  

=(  

r  

1

​  

 

kQ

​  

−  

r  

2

​  

 

4kQ

​  

)−(  

r  

2

​  

 

kQ

​  

−  

r  

2

​  

 

4kQ

​  

)

r  

1

​  

 

kQ

​  

−  

r  

2

​  

 

kQ

​  

 

=kQ(  

r  

1

​  

 

1

​  

−  

r  

2

​  

 

1

​  

)=V

Hence, we also obtain that potential difference does not depend on charge of outer sphere.

∴P.d. remains same.

Explanation: