A doubly ionized carbon atom (with charge 2e) is located at the origin of the x

Question

A doubly ionized carbon atom (with charge 2e) is located at the origin of the x axis, and an electron (with charge -e) is placed at x = 5.01 cm. There is one location along the x axis at which the electric field is zero. Give the x coordinate of this point in cm. Assume that the potential is defined to be zero infinitely far away from the particles. Unlike the electric field, the potential will be zero at multiple points near the particles. Find the two points along the x axis at which the potential is zero, and express their locations along the x axis in cm, starting with the point which is farther away from the origin.

Explanation / Answer

let at x1 the electric field is zero

x1 > x

k*2e/x1^2 = k*e/(x1-x)^2

2/x1^2 = 1/(x1-5.01)^2

x1 = 17.1 cm <<--------answer

+++++++++++++++

for potential to be zero

at point x1 >x and x1 <x the potentail is zero

x1>x

k*2e/x1 = k*e/(x1-x)

2/x1 = 1/(x1-5.01)

x1 = 10.2 cm <<--------answer

x1 <x

k*2e/x1 = k*e/(x-x1)

2/x1 = 1/(5.01-x1)

x1 = 3.34 cm <<--------answer

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