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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 yaxis? 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.
 Fall '08
 Milsom

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