10 A doubly ionized carbon atom (with charge +2e) Is located at the origin of th

Question

10

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 = 801 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 (he 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

q1 = charge on carbon = 2 e = 2 x 1.6 x 10-19 = 3.2 x 10-19

q2 = charge on electron = e = 1.6 x 10-19 C

r = distance between carbon and electron = 8.01 cm = 0.0801 m

let the zero electric field point be distance "d" away from the electron on its right

For zero electric field

E1 = E2

k q1 / (r + d)2 = k q2/d2

3.2 x 10-19 /(0.0801 + d)2 = 1.6 x 10-19/d2

d = 0.193 m

X-coordinate of the point = r + d = 0.0801 + 0.193 = 0.273 m = 27.3 cm

let the zero electric potential point be distance "d" away from the electron on its right

For zero electric potential at a point

V1 + V2 = 0

k q1 / (r + d) + k q2/d = 0

3.2 x 10-19 /(0.0801 + d) - 1.6 x 10-19/d= 0

d = 0.0801 m

X-coordinate of the point = r + d = 0.0801 + 0.0801 = 0.1602 m = 16.02 cm

let the zero electric potential point be distance "d" away from the carbon on its right

For zero electric potential at a point

V1 + V2 = 0

k q1 / d + k q2/(r - d) = 0

3.2 x 10-19 /d - 1.6 x 10-19/(0.0801 - d)= 0

d = 0.0534 m

X-coordinate of the point = 0.0534 = 5.34 cm

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