Question

A point particle that has a charge of +11.9 nC is at the origin.

(a) What is (are) the shape(s) of the equipotential surfaces in the region around this charge?

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(b) Assuming the potential to be zero at r = ∞, calculate the radii of the five surfaces that have potentials equal to 20.5 V, 42.5 V, 64.5 V, 86.5 V, and 108.5 V, and sketch them to scale centered on the charge. (Give your answer to at least two decimal places.)

V (V)	20.5	42.5	64.5	86.5	108.5
r (m)

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(c) Are these surfaces equally spaced? Explain your answer.

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(d) Estimate the electric field strength between the 42.5-V and 64.5-V equipotential surfaces by dividing the difference between the two potentials by the difference between the two radii.
E_est ≈  V/m

Compare this estimate to the exact value at the location midway between these two surfaces.

Answer 1

(A) equipotential surfaces are spheres whose center is the given charge.

(B) V = k Q / r

V = (9 x 10^9)(11.9 x 10^-9)/r

r = 107.1 / V

V = 20.5 V => r = 5.22 m

V = 42.5 V => r = 2.52 m

V = 64.5 V => r = 1.66 m

V = 86.5 V => 1.24 m

V = 108.5 V => r = 0.987 m

(C) no, theses are not equally spaced as we can see from the images.

(D) E = - (64.5 - 42.5) / (1.66 - 2.52)

E = 25.6 N/C

E_exact = kq /r^2 = (9 x 10^9) (11.9 x 10^-9)/ ((1.66 +2.52)/2)^2

= 24.5 N/C