A charge 'Q' is distributed over two con...

A charge 'Q' is distributed over two concentric hollow spheres of radii 'r' and 'R' (gtr) such that the surface densities are equal. Find the potential at the common centre.

`(Q(R^(2)+r^(2)))/(4piepsilon_(0)(R+r))`

`(Q)/(R+r)`

zero

`(Q(R+r))/(4piepsilon_(0)(R^(2)+r^(2)))`

Text Solution

Verified by Experts

The correct Answer is:

Since surface densities are equal
`(q_(1))/(4pir^(2))=(q_(2))/(4piR^(2))`, Where `q_(1)+q_(2)=Q`
`(q_(1))/(r^(2))=(q_(2))/(R^(2))`, therefore `(q_(1)+q_(2))/(r^(2)+R^(2))=(Q)/(r^(2)+R^(2))`
`q_(1)=(Q)/(R^(2)+r^(2))xxr^(2),q_(2)=(Q)/(R^(2)+r^(2))R^(2)`
Potential at the common cnetre , is
`V=(q_(1))/(4piepsilon_(0)r)+(q_(2))/(4piepsilon_(0)R)=(1)/(4piepsilon_(0))((q_(1))/(r)+(q_(2))/(R))`
`=(1)/(4piepsilon_(0))((Q)/(R^(2)+r^(2))xx(r^(2))/(r)+(Q)/(R^(2)+r^(2))(R^(2))/(R))=(Q(R+r))/(4piepsilon_(0)(R^(2)+r^(2)))`

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A charge Q is distributed over two concentric hollow spheres of radii (r) and (R) gt (r) such the surface densities are equal. Find the potential at the common centre.

`Q/(4 pi epsilon_0) xx ((r + R))/((R + r)^2)`

`(Q(R^2 + r)^2)/(4pi epsilon_0(r + R))`

`(Q(r + R))/(4pi epsilon_0(R^2 + r^2))`

none of these

A charge q is distributed over two concentric hollow sphere of radii a and b(bgtc) such that the surface densities are equal.Find the potential at the common centre.is

zero

`(q)/(4piepsilon_(0))((a+b))/((a^(2)+b^(2)))`

`(q)/(4piepsilon_(0))[(1)/(a)+(1)/(b)]`

`(q)/(4piepsilon_(0))[(a+b)/((a^(2)+b^(2)))]`

A total charge Q is distributed over two concentric hallow uniform sphere of radii a and b, (bgta) such a way that their surface charge densities are qual. The potential at the common centre is given by :

`(Q)/(4piepsilon_(0))((a+b))/((a^(2)+b^(2))`

`(Q)/(4piepsilon_(0))((a-b))/((a^(2)+b^(2))`

`(Q)/(4piepsilon_(0))((a-b))/((a+b)^(2))`

`(Q)/(4piepsilon_(0))((b-a))/((a+b)^(2))`