241_hw03 - Physics 241 - Electric Potential and Potential...

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Unformatted text preview: Physics 241 - Electric Potential and Potential Energy 1: a: A charge Q is fixed in place. A charge -q of mass m1 is released from ‘ rest a distance d from Q. Determine the velocity of —q as a function of its distance x from Q. (Yes, you solved this on the electrostatics assignment but this time use energy techniques.) b: Redo part a: but this time charge Q (of mass m2) is free to move. Note that you will need to conserve more than energy here. 2: Three charges are arranged in an equilateral triangle of side 10’8m. Clockwise from lower left they are 2710, —-4nC and 3nO’. a: Determine the voltage at the origin. What does this tell you? b: Determine the electrical potential energy of the system. What does this c: Would it take positive or negative work to move the top charge further tell you? i up the y-axis? Explain. Determine the minimum work required if you move it a distance of 0.5 x 10‘3m. Q3 3: Two electrons are fixed in place with L = 0.01m. A third electron is shot towards them from infinitely far away along their perpendicular bisector. The third electron comes to rest emactly between the two. Determine the initial speed of the third electron. 4: The equipotentials (10V apart) are shown in a region of space. Five points are also marked on one of the equipotential lines on the diagram (see last page of assignment). The potential on that line is 100V. 3.: If an electron were released at the middle point, it would accelerate straight to the left. Label the electric potential on the other equipotential lines. b: Draw electric field lines through each point and follow them as far as diagram. you can on the c: Where is the electric field the strongest? Explain. Note that it is not possible to use the electric field lines to answer this question since you have not necessarily drawn a sufficient number of lines to see the field correctly. 5: There are two infinite planes of charge separated by a distance D. The top plane has atop = 0'0 and the bottom plane has 050mm = —2cro. Draw the electric field and the equipotential lines. Use the diagram at the end of the assignment. (Yes, you solved for the electric field for this arrangement on the electrostatics assignment.) 6: Draw the electric field lines and equipotential lines for a point charge —gQ near a point charge Q. ‘ 7: A point charge 2Q is at the origin and a point charge —Q is at (d, 0,0). a: Determine the electric potential for any point in the xy plane. b: Determine the radius and location of the circle on which V = 0. Does yoiir answer make sense? Explain. If we extend this to three dimensions, would the equipotential volume with V = 0 be spherical? Explain. c: Determine Ez($,y) and Ey($,y). 8: Let’s solve this problem from the electrostatics assignment again. Thje bar here has A = A0. ‘ a: Determine the electric potential at point P. b: Determine the electric field at point P using your result from a. Note that D is a coor— dinate variable here and that D = —:?: so your answer will “appear” to be the negative of what we got previously. P L D 9: Determine V(r) everywhere in space for a sphere of radius R with a constant charge density of p = p0. You will need to use V = — E - dr so that the potential is zero at 7‘ = 00. 10: Dust grains (1‘ 2 1pm )in Saturn’s rings are in a region of dilute ionized gas. Thus, these dust grains can pick up electrons. If the potential at the surface of ‘a dust grain is —4OOV, determine the number of electrons on the dust grain. Assume that the electrons are distributed spherically and that the individual dust grains are far enough apart that their electrons don’t affect each other. ! 11: You have two conducting spheres. Sphere A has RA = 0.2m and Q A = 10—70. Sphere B has R3 = 0.3m and Q3 = —2 X 10‘7C. The spheres are touched together and then separated far apart. What is the magnitude of the electric field at the surface of each sphere? ...
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This note was uploaded on 01/19/2011 for the course PHYS 241 taught by Professor Milsom during the Fall '08 term at University of Arizona- Tucson.

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241_hw03 - Physics 241 - Electric Potential and Potential...

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