Question

Is potential at centre of a spherical capacitor equal to potential difference between the shells?​

Answer 1

ANSWER

Radius of the outer shell = r1

Radius of the inner shell = r2

The inner surface of the outer shell has charge +Q.

The outer surface of the inner shell has induced charge −Q.

Potential difference between the two shells is given by,

V=

4πε

o

r

2

Q

−

4πε

o

r

1

Q

Where,

ε

o

= Permittivity of free space

V=

4πε

o

r

2

Q

−

4πε

o

r

1

Q

V=

4πε

o

Q

[

r

2

1

−

r

1

1

]

V=

4πε

o

r

1

r

2

Q(r

1

−r

2

)

Capacitance of the given system is given by,

C=

V

Q

C=

r

1

−r

2

4πε

o

r

1

r

2

Hence, proved.

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