A nonconducting sphere with radius a is concentric with and surrounded by a conducting spherical shell with inner radius b and outer radius c. The inner sphere has a negative charge uniformly distributed throughout its volume, while the spherical shell has no net charge. The potential V (r) as a function of distance from the center is given by

Options

A.
B.
C.
D.

Answer

b

Explanation

Consider a spherical shell of ratio `r` and thickness `dr`
Resistance of this shell is `dR = (rhodr)/(4pi r^(2))`
Total resistance
`R = int dR = underset(r_(a))overset(r_(b))(int) (rho dr)/(4pir^(2)) = (rho)/(4pi) [(1)/(r_(a))-(1)/(r_(b))]`

Current `I = (V_(a) - V_(b))/(R)`
The electric field intensity at the location of shell
or `E = (J)/(alpha) = (I//pi r^(2))/(1//rho) = (rho I)/(4pi r^(2))`
Where `J` is the current density and `sigma` is the electrical conductivity of the conducting meterial
`:. E = (rho)/(2pi r^(2)) xx((V_(a) - V_(b))/(R)) = (rho)/(2pi r^(2))((V_(a) - V_(b)) xx 4pi)/(rho((1)/(r_(a)) - (1)/(r_(b))))`
`=((V_(a) - V_(b)))/(r^(2)[(1)/(r_(a))-(1)/(r_(b))])`
As current `I` is zero for `r lt r_(a) and r gt r_(b)` so variation of E and r will be represented in the curve shown in in option b