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 = 5.76 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.

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

q1 = 2e @ x= 0
q2 = -e @ x= 5.76 cm

E = k Q/r^2
Let the point where Electric field is zero be x cm from q1.
Distance from q2 = 5.76 cm - x

E = k ( 2e/ x^2 - e/ (5.76 - x)^2)
2 / x^2 = 1/(5.76 - x)^2)
2* (5.76 - x)^2 = x^2
Solving for x
x = 19.66 cm
Electric field is zero @ x = 19.66 cm

(b)

E.P = k Q/r
Let the point where Electric Potential is zero be x cm from q1.
Distance from q2 = 5.76 cm - x

E.P = K*2e / x - k * e /(5.76 - x)
2/x = 1/(5.76 - x)
2* (5.76 - x) = x
Solving for x
x = 3.84 cm

Let the point where Electric Potential is zero be x cm from q2.
Distance from q1 = 5.76 cm + x

E.P = K*2e / (5.76 + x) - k * e /x
2/(5.76 + x)  = 1/x
2*x = 5.76 + x
Solving for x
x = 5.76 cm
Therefore Distance from origin = 5.76 + 5.76 = 11.52 cm

Electric potential is zero @ x = 11.52 cm and @ x = 3.84 cm

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.