Question 9 of 20 Map a Sapling Learning macmillan learning A doubly ionized carb

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Question 9 of 20 Map a Sapling Learning macmillan learning 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 8.76 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. 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 xaxis at which the potential is zero, and express their locations along the xaxis in cm, starting with the point which is farther away from the origin. Farther Point: Number cm Closer Point: Number cm

Explanation / Answer

let the electric field be 0 at point distance "d" away from electron towards its right

for electric field to be 0

Electric field by ionised carbon = Electric field by electron

k (2e)/(d + 0.0876)2 = k (e)/d2

2/(d + 0.0876)2 = 1/d2

d = 0.318 m = 31.8 cm

X-coordinate : = 8.76 + 31.8 = 40.56 cm

let the point of zero potential be between the two charges at distance "d" from carbon

between the two charges :

potential by ionised carbon = Potential by electron

k(2e)/d= k e /(0.0876 - d)

d = 0.0584 m = 5.84 cm

consider the zero potential point to the right of electron at distance "d"

potential by ionised carbon = Potential by electron

k(2e)/(0.0876 + d)= k e /d

d = 0.0876 = 8.76 cm

X-coordinate = 8.76 + 8.76 = 17.52

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