Question

A uniform charge of +47.0 μC is on a thin circular ring lying in an xy plane and centered on the origin. The ring's radius is 8.90 cm. If point A is at the origin and point B is on the z axis at z = 3.70 cm, what is V_B – V_A (in V)?

Answer 1

Here:
Q = 47*10^-6 C
z= 3.7 cm= 0.037 m
a=8.9 cm= 0.089 m

VB = K*Q /sqrt(Z^2+a^2)
= (9*10^9)*(47*10^-6) / sqrt (0.037^2 + 0.089^2)
= 423000 / 0.0964
= 4.39 * 10^6 V

for VA, z= 0
VA = K*Q /sqrt(Z^2+a^2)
= (9*10^9)*(47*10^-6) / 0.089
= 423000 / 0.089
= 4.75 * 10^6 V

VB-VA = 4.39 * 10^6 - 4.75 * 10^6 V
= 3.6*10^5 V
Answer: 3.6*10^5 V

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