1)A doubly ionized carbon atom (with charge 2e) is located at the origin of the

Question

1)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 = 3.51 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. ........2) 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. ........ 2) Farther Point: .... 3)Closer Point:

Explanation / Answer

Given,

q1 = +2e and q2 = -e where e is charge of electron and = 1.6 x 10-19 C

q1 is located at x = 0 and q2 a x = 3.51 cm

1)We need to find out the coordinates of a point where E field is zero. Let E1 and E2 be the E fields due to charges Q1 and Q2 respectively. For point P at which E field is zero, we can write:

E1 + E2 = 0

E1 = - E2

K(2e) / x2 = -K(-e) / ( x - 3.51)2

2/x2 = 1/ ( x - 3.51)2

2( x2 + 12.32 - 7x) =  x2

x2 + (-14) x+ 24.64 = 0

x = [14 +- sqrt (196 -98.6)]/2 = 2,12

The quadratic eqn gave two values of x where E field is zero at x = 2cm and 12cm

(2) Now we have find the x coordinates of two points where potential is zero.

Kq1/x1+ Kq2/x2= 0

K(2e)/x = -K(-e)/(x - .3.51)

2/x = 1/(x - 3.51)

2x - 7.02 = x gives us x = 7.02

(for getting another point where electric potential is zero)

2x -7.02 = -x

x = 2.34

hence the trwo points at whcih potential will be zero are x = 7.02cm and x = 2.34 cm

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