For a single, isolated point charge carrying a charge of q = 1.92 x 10^-11 C, on

Question

For a single, isolated point charge carrying a charge of q = 1.92 x 10^-11 C, one equipotential surface consists of a sphere of radius 0.0224 m centered on the point charge as shown. What is the potential on this surface? You would like to draw an additional equipotential surface, which is separated by 4.32 V from the previously mentioned surface. How far from the point charge should this surface be? This surface must also meet the condition of being farther from the point charge than the original equipotential surface.

Explanation / Answer

(i)   The electric potential at a circular equipotential surface created at a distance of r = 0.0224 m

V = k*q / r , where k = 8.9*10^9 N*m^2 / C^2

=> V = 8.9*10^9 * 1.92*10^-11 / 0.0224 = 7.63 V

(ii) For the new equipotential surface being farther from the previous one

i.e. for r' > r , V' = V - 4.32 = 7.63 - 4.32 = 3.31 V

Using,   V' = k*q / r'   , where k = 8.9*10^9 N*m^2 / C^2

=> r' = k*q / V' =   8.9*10^9 * 1.92*10^-11 / 3.31 = 0.0516 m

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