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 = 1.26 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 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

field between charges is on same direction due to both charges. so never zero. also on -x axis field due to +2e is always greater. So, field will be zero only somewhere right to the electron on +ve x axis.

k2e/x2 + k(-e)/(x - 1.26)2 =0

(x - 1.26)* sqrt(2) = x => x = 4.302 cm

potential on -x axis is always +ve

for farther point, potential will be zero right to electron

k2e/x - ke/(x-1.26) = 0 => 2(x - 1.26) = x => x = 2.52 cm

for closer point, potential will be zero in between charges,

k2e/x - ke/(1.26 - x) = 0 => 2(1.26 - x) = x => x = 0.84 cm

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