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=726cm. There is one location along the x axis at which the electric field is zero Give the x coordinate of this point in cm. Number 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. Farther Point Number cm Closer Point: Number cm

Explanation / Answer

q1 = +2e = 2*1.6*10^-19 C = 3.2*10^-19 C

x1 = 0

q2 = -e = -1.*10^-19 C

x2 = 7.26 cm = 0.0726 m

at point on x > x2 axis E = 0

E1 = E2

k*q1/x^2 = k*q2/(x-x2)^2

3.2*10^-19/x^2 = 1.6*10^-19/(x-0.0726)^2

x = 24.8 cm

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if x < x2

V1 + V2 = 0

k*q1/x + k*q2/(x2-x) = 0

q1/x + q2/(x2-x) = 0

3.2*10^-19/x - 1.6*10^-19/(0.0726-x) = 0

x = 4.84 cm

x > x2

V1 + V2 = 0

k*q1/x + k*q2/(x-x2) = 0

q1/x + q2/(x-x2) = 0

3.2*10^-19/x - 1.6*10^-19/(x-0.0726) = 0

x = 14.5 cm

Farther point x = 14.5 cm

Closer point x = 4.84 cm

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