Electric Potential Energy & Potential Solutions from Essential Physics Ch. 17, Study notes of Physics

Download Electric Potential Energy & Potential Solutions from Essential Physics Ch. 17 and more Study notes Physics in PDF only on Docsity! Essential Physics Ch. 17 (Electric Potential Energy and Potential) Solutions to Sample Problems PROBLEM 1 – 10 points Two charges are placed on the x-axis. The charge at x = -3d has a charge of –2Q, 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 –2Q charge [ X ] between the charges [ X ] to the right of the +Q charge Because one charge has twice the magnitude of the other we’re looking for locations twice as far from the –2Q 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: 1 2 0V V+ = 1 2 0V V+ = ( 2 ) 0 ( 3 ) 3 k Q kQ x d d x − + = − − − ( 2 ) 0 ( 3 ) 3 k Q kQ x d x d − + = − − − 2 1 3 3x d d x = + − 2 1 3 3x d x d = + − 6 2 3d x x d− = + , so 3 3d x= and x d= + 2 6 3x d x d− = + , so 9x 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 –2Q 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. Essential Physics Ch. 17 (Electric Potential Energy and Potential) Solutions to Sample Problems PROBLEM 2 – 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 –Q 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 –Q 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. 4 3 7kQ kQ kQ kQ kQV 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 7kQV d = + while configuration C has a potential at the origin of 4kQV 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 2kq qU r = terms, one for each pair of charges, to get for configuration A: ( ) 2(7 ) ( )(7 ) 2 2 kQ Q kQ Q k Q Q kQU d r r d − − − = + + = . Doing the same thing for the other configurations results in positive answers.