Two spherical conductors A and B of radii 1mm and 2mm are separated by a distance of 5 cm and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres A and B is

Options

A. `4:1`
B. `1:2`
C. `2:1`
D. `1:4`

Answer

C

Explanation

`V=K.(Q)/(R ) " " (V)/(2)=K.(Q)/(2R)=K.(Q)/(R )`
`(1)/(2) (K. (Q)/(R ))=K. (Q)/(d) " " d=2R`
When the two conducting spheres are connected by a conducting wire, charge will flow from one sphere (having higher potential) to other (having lower potential) till both acquire the same potential.
There fore, `E=(V)/(r )`
`rArr (E_(1))/(E_(2))=(r_(2))/(r_(1))=(2)/(1)=2:1`