Question

Two metallic spheres of radii `R and 2 R` are charged so that both of these have same surface charge density, `sigma` . If they are connected to each other with a conducting wire, in which direction will the charge flow and why ?

Answer 1

Let `R_(1) = R, R_(2) = 2R`.
If `Q_(1) and Q_(2)` are the respective charges, then as
`sigma = (Q_(1))/(4pi R_(1)^(2)) = (Q_(2))/(4pi R_(2)^(2))`
`:. (Q_(1))/(Q_(2)) = (R_(1)^(2))/(R_(2)^(2)) = ((R )/(2R))^(2) = (1)/(4)`
`As V_(1) = (Q_(1))/(4pi in_(0) R_(1)) , V_(2) = (Q_(2))/(4pi in_(0) R_(2))`
`:. (V_(1))/(V_(2)) = (Q_(1))/(Q_(2)) , (R_(2))/(R_(1)) = (1)/(4) xx (2)/(1) = (1)/(2)`
Clearly, `V_(2) gt V_(1)`. Hence charge flows from sphere of radius `2 R` to sphere of radius R.