Download Electric Potential Energy & Potential Solutions from Essential Physics Ch. 17 and more Study notes Physics in PDF only on Docsity!
PROBLEM 1 โ 10 points
Two charges are placed on the x-axis. The charge at x = -3d has a charge of โ2Q, while the charge at +3d has a charge of +Q.
[2 points] (a) The net electric potential due to the two charges is zero at at least one location on the x-axis near the two charges. In which region(s) is there such a point on the x-axis, where the net electric potential is zero a finite distance from the charges? Select all that apply.
[ ] to the left of the โ2Q charge
[ X ] between the charges
[ X ] to the right of the +Q charge
Because one charge has twice the magnitude of the other weโre looking for locations twice as far from the โ2Q charge as from the +Q charge. There is one such location between the charges and another to the right of the +Q charge.
[5 points] (b) Determine the location of one such point on the x-axis near the charges where the net electric potential is zero.
Between the charges: To the right of the +Q charge: V 1 (^) + V 2 = 0 V 1 (^) + V 2 = 0 ( 2 ) 0 ( 3 ) 3
k Q kQ x d d x
k Q kQ x d x d
x 3 d 3 d x
x 3 d x 3 d
6 d โ 2 x = x + 3 d , so 3 d = 3 x and x = + d 2 x โ 6 d = x + 3 d , so x = + 9 d
[3 points] (c) Are there any points near the charges, but not on the x-axis , where the net electric potential due to the point charges is zero? Explain.
Yes, there are plenty of such points. Potential is a scalar, so there is no direction to worry about. Every point that is twice as far from the โ2Q charge as it is from the +Q charge will work. There is an oval equipotential line, passing through x = +d and x = +9d that connects all of these points.
PROBLEM 2 โ 15 points
Three configurations of point charges are shown. Each charge is located a distance d from the origin. In each case the origin is located at the intersection of the axes. The electric potential from a single charge is defined to be zero an infinite distance from the charge, and the electric potential associated with two charges is also defined to be zero when the charges are infinitely far apart.
[4 points] (a) In configuration A , imagine that the +Q and โQ charges are placed at the locations shown, and then the +7Q charge is brought into the picture and placed at its location. Does bringing in the +7Q charge cause the potential energy of configuration A to increase, decrease, or stay the same? Briefly explain.
The potential energy stays the same. The +7Q charge interacting with the +Q charge has a positive potential energy, while the interaction of the +7Q charge interacting with the โQ charge has a negative potential energy. These have the same magnitude because the distances involved are equal.
[4 points] (b) In configuration B , what is the electric potential at the origin because of the four charges? You can express this in terms of k, Q, and d. kQ kQ 4 kQ 3 kQ 7 kQ V d d d d d
[3 points] (c) Rank the three configurations based on the electric potential at the origin due to the charges, from largest to smallest.
[ ] A>B>C [ ] A>C>B [ X ] A=B>C [ ] B>A>C [ ] B>C>A [ ] C>A>B [ ] C>B>A [ ] C>A=B Both configurations A and B have a net potential at the origin of 7 kQ V d
= + while
configuration C has a potential at the origin of 4 kQ V d
[4 points] (d) In one, and only one, of the configurations the total potential energy is negative. Which configuration is this?
[ X ] A [ ] B [ ] C
Briefly explain your answer: Add up all the^1
kq q U r
= terms, one for each pair of charges, to
get for configuration A:
( ) (7 ) ( )(7 )^2
kQ Q (^) kQ Q k Q Q kQ U d r r d
= + + =. Doing the same thing
for the other configurations results in positive answers.
