two metal spheres of radii `R_(1)` and `R_(2)` are charged to the same potential. The ratio of charges on the spheres is

Options

A. `(R_(1))/(R_(2))`
B. `(R_(2))/(R_(1))`
C. `sqrt(((R_(1))/(R_(2))))`
D. `(R_(1)^(2))/(R_(2)^(2))`

Answer

B

Explanation

Potential at the surface of spherical conductor of radius R carrying charge Q, `V_(S) = (Q)/(4pi epsilon_(0)R)`
Let `Q_(1)` and `Q_(2)` are the charge on two spherical conductor of radii `R_(1)` and `R_(2)` respectively. When these two charged spherical conductors connected by a wire, the potential at their surfaces becomes equal.
`:. V_(S_(1)) = V_(S_(2))`
`(Q_(1))/(4pi epsilon_(0)R_(1)) = (Q_(2))/(4pi epsilon_(0)R_(2))` or `(Q_(1))/(Q_(2)) = (R_(1))/(R_(2))` ....(i)
Surface charge density, `sigma = ("Charge")/("Area")`
`:. (sigma_(1))/(sigma_(2)) = (((Q_(1))/(4pi R_(1)^(2))))/(((Q_(2))/(4pi R_(2)^(2)))) = (Q_(1))/(Q_(2)) xx (R_(2)^(2))/(R_(1)^(2)) = (R_(1))/(R_(2)) xx (R_(2)^(2))/(R_(1)^(2)) = (R_(2))/(R_(1))` (Using (i))