The electric potential (V) produced by a point charge with a charge of magnitude Q, at a point a distance r away from the point charge, is given by the equation:
[tex]V = \frac{kQ}{r}[/tex]
Here,
k = Coulomb's constant
Q = Charge
r = Distance
If we rearrange the equation to find the distance we have,
[tex]Q=\frac{Vr}{k}[/tex]
[tex]Q = \frac{(100)(5*10^{-2})}{9*10^9}[/tex]
[tex]Q = 5.55*10^{-10} C[/tex]
Now the value of the charge density is equivalent to the charge on the surface area of the sphere this is
[tex]\gamma = \frac{Q}{A_s}[/tex]
[tex]\gamma = \frac{Q}{4\pi r^2}[/tex]
[tex]\gamma = \frac{ 5.55*10^{-10}}{4\pi (5*10^{-2})^2}[/tex]
[tex]\gamma = 1.76*10^{-8} C/m^2[/tex]
