A uniformly charged ring with total charge q = 3.50 µC and radius R = 20.0 cm is

Question

A uniformly charged ring with total charge q = 3.50 µC and radius R = 20.0 cm is placed with its center at the origin and oriented in the xy plane. What is the difference between the electric potential at the origin and the electric potential at the point (0, 0, 40.0 cm)?

A uniformly charged ring with total charge 3.50 pC and radius R = 20.0 cm is placed with its center at the origin and oriented in the xy plane, what is the difference between the electric potential at the origin and the electric potential at the point (0, 0, 40.0 cm)? 8.69e4 e8 87000 V

Explanation / Answer

Electric potential due to a charged ring on its axis is given by :

V = k*q/sqrt(R^2 + z^2)

where k = 9*10^9

q = 3.5*10^-6 C

R = 20 cm = 0.2 m

So, at z = 40 cm = 0.4 m

V = 9*10^9*(3.5*10^-6)/sqrt(0.2^2 + 0.4^2)

= 7.04*10^4 V

Now, Potential at the center of the circle : <---- at this point z = 0

V' =  9*10^9*(3.5*10^-6)/sqrt(0.2^2 + 0^2)

= 1.575*10^5 V

So, potential difference between those two points :

V - V' = 7.04*10^4 - 1.575*10^5 = -87000 V <------answer

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