For each of the following cases, write a symbolic expression for the voltage and

Question

For each of the following cases, write a symbolic expression for the voltage and an expression for the electric field at the center of the circle. Based on your results in (a) - (f), which of the following statements are correct? Two points that have the same voltage have the same electric field. Two points that have the same electric field have the same voltage. Knowing the voltage at a single point does not determine the electric field at that point. Knowing the electric field at a single point does not determine the voltage at that point.

Explanation / Answer

a)

v = kQ/R

E = -kQ/R^2

b)

V = kQ/2R + kQ/2R = kQ/R

E = kQ/2R^2 - kQ/2R^2 = 0

c)

V = kQ/3R + KQ/3R + KQ/3R = KQ/R

E = kQ/3R^2 - kQ/3R^2 - kQ/3R^2 = -kQ/3R^2 (down wards)

d)

V = kQ/2R - KQ/2R = 0

E = KQ/2R^2 + kQ/2R^2 = KQ/R^2

e)

V = -KQ/2R - kQ/2R + KQ/R = KQ/R

E = KQ/2R^2 - KQ/2R^2 - KQ/R^2 = -KQ/R^2

f)

V = KQ/R - KQ/R + KQ/R - KQ/R = 0

E = KQ/R^2 - KQ/R^2 + KQ/R^2 - KQ/R^2 = 0

1)

correct

a & e

2) correct

3)

incorrect

4)

correct

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