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Concentric metallic hollow spheres of ra...

Concentric metallic hollow spheres of radii R and 4R hold charges `Q_1 and Q_2` respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference `V(R)- V(4R)` is :

A

`(3Q_(1))/(16piepsilon_(0)R)`

B

`(3Q_(2))/(4piepsilon_(0)R)`

C

`(Q_(2))/(4piepsilon_(0)R)`

D

`(3Q_(1))/(4piepsilon_(0)R)`

Text Solution

Verified by Experts

The correct Answer is:
A
`V_("inner")=(KQ_(1))/(R)+(KQ_(2))/(4R)`
`V_("outer")=(KQ_(1))/(4R)+(KQ_(2))/(4R)`
Potential difference
`DeltaV=V_("inner")-V_("outer")`
`=(3)/(4).(KQ_(1))/(R)=(3)/(16piepsilon_(0)).(Q_(1))/(R)`.
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