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A solid sphere of radius R(1) and volume...

A solid sphere of radius `R_(1)` and volume charge density `rho = (rho_(0))/(r )` is enclosed by a hollow sphere of radius `R_(2)` with negative surface charge density `sigma`, such that the total charge in the system is zero . `rho_(0)` is positive constant and `r` is the distance from the centre of the sphere . The ratio `R_(2)//R_(1)` is

A

`sigma// R_0`

B

`sqrt(2sigma//rho_0)`

C

`sqrt(rho_0//2sigma)`

D

`rho_0//sigma`

Text Solution

Verified by Experts

The correct Answer is:
C
Total charge in the inner sphere
`Q_1=int_0^(R_1)rhodV =int_0^(R_1) (rho_0)/r(4pir^2)dr = 4pi(R_1^2)/2rho_0`
Total charge on outer shell
`Q_2 = -4pi R_2^2 sigma`
Since, `Q_1+Q_2=0`
`4pi (R_1^2)/(2)rho_0=4piR_2^2sigmaimplies R_2^2/(R1^2)=rho_0/(2sigma)implies R_2/R_1=sqrt((rho_0)/(2sigma))`
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