Two metal spheres `A` and `B` of different sizes are charged such that the electric potential is the same at the surface of each. Sphere A has a radius three times that of sphere `B`. If `E_(A)` and `E_(B)` be the electric field magnitudes at the surface of each sphere, then `E_(B)//E_(A)` is

Answer

3

Explanation

As `V_(A) = V_(B) implies (K Q_(B))/(R_(B)) = (K Q_(A))/(R_(A))`
`= (K Q_(B))/(3R_(A)//3) = (KQ_(A))/(R_(A))`
or `Q_(A) = 3Q_(B)` or `(Q_(A))/(Q_(B)) = (1)/(3)`
Further, `(E_(B))/(E_(A)) = (Q_(B)//R_(B)^(2))/(Q_(A)//R_(A)^(2)) = (1)/(3) (3)^(2) = 3`