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 = 7.26 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 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

so -e will have field going into it and the 2e will have field going away from it we want these to be in opposite directions so lets consider to the right of the electron then the field from -e is to the left and the field from 2e is to the right. if they are going to cancel E1 = E2 k 2e/x^2 =ke/(x-7.26E-2)^2 cross multiply 2(x-*7.26E-2)^2= x^2 solve for x x= 24.78 cm cm for the potential there is no direction so we dont have to consider places so we want V1 = V2 k 2e/abs(x) = ke /abs(x-7.26E-2) cross multiple 2*abs(x-7.26E-2)=abs(x) solve for x x=4.84 cm and 14.52 cm

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