(a) Charge on sphere A, `q_(A)` = Charge on sphere B, `q_(B) = 6.5 × 10^(−7) C`
Distance between the spheres, r = 50 cm = 0.5 m
Force of repulsion between the two spheres,
`F = (q_(A) q_(B))/(4pi epsi_(0)r^(2))`
Where,
`epsi_(0)` = Free space permittivity
`(1)/(4 pi epsi_(0)) = 9 xx 10 ^(9) Nm^(2) C^(-2)`
` therefore F = ( 9xx 10^(9) xx (6.5 xx 10 ^(-7))^(2))/((0.5)^(2)) `
`= 1.52 xx 10^(-2) N`
Therefore, the force between the two spheres is `1.52 × 10^(−2) N`.
(b) After doubling the charge, charge on sphere A, `q_(A)` = Charge on sphere B, `q_(B) = 2 × 6.5 × 10^(−7) C = 1.3 × 10^(−6) C`
The distance between the spheres is halved.
`therefore r =( 0.5)/(2)= 0.25 m`
`= (9 xx 10^(9) xx 1.3 xx 10 ^(-6) xx 1.3 xx 10 ^(-6)) /(( 0.25)^(2))`
`= 16 × 1.52 × 10^(−2)`
= 0.243 N
Therefore, the force between the two spheres is 0.243 N.