At a distance of `5 cm and 10 cm` outward from the surface of a uniformly charged solid sphere, the potentials are `100 V and 75 V`, repectively. Then.

Options

A. Potential at its surface is `150 V`
B. the charge on the sphere is `(5//3) xx 10^-10 C`
C. the electric field on the surface is `1500 Vm^-1`
D. the electric potential at its center is `0 V`

Answer

a.,c.

Explanation

`V = (1)/(4 pi epsilon_0) q/((R + d))`
`R` is radius, and `d` is distance from surface
`100 = K q/((R + 5) xx 10^-2))`…(i)
`75 = K q/((R + 10) xx 10^-2))` ….(ii)
From (i) and (ii). `R = 10 cm` and `Q = (50)/(3) xx 10^-10 C`
Potential at surface is
`V_0 = (k Q)/(R) = (9 xx 10^9 xx 50)/(10 xx 10^-2 xx 3) xx 10^-10 = 150 V`
Electric field on surface is `E_0 = (k Q)/(R^2) = 1500 Vm^-1`
Potential at the center is `V_C = (3)/(2) V_0 = 225 V`.