Question

A system consists of two isolated conducting spheres. kept at infinite distance sphere X has radius 2R/3 and charge 12 uC and Sphere Y has radius R/3 and charge -3 uC. if the switch is closed then find charges on X and Y. ​

Answer 1

A system consists of two isolated conducting spheres. kept at infinite distance sphere X has radius 2R/3 and charge 12 μC and Sphere Y has radius R/3 and charge -3 μC.

To find : if the switch is closed then find the charges on X and Y.

solution : if switch is closed, potential of each sphere will be same.

i.e., potential of Sphere X = potential of Sphere Y.

let charge on sphere X is q₁ and sphere Y is q₂

so, Kq₁/(2R/3) = K(q₂)/(R/3)

⇒q₁/q₂ = 2

⇒q₁ = 2q₂........(1)

from conservation of charge,

initial total charge = final total charge

⇒12μC - 3μC = q₁ + q₂

⇒q₁ + q₂ = 9μC ......(2)

from equations (1) and (2) we get,

q₁ = 6μC and q₂ = 3μC

Therefore the charges on X and Y are 6μC and 3μC respectively.