Download PHYS 196 Class Problem 1

PHYS 196 Home Work 5A
1. What is the electric potential at a point 4.0m away from a 2.0C point charge, assuming the potential is
zero at infinity? How much work is required to bring a 3.0C point charge from infinity to this point?
The next three problems refer to two point charges on the x–y plane where coordinates are measured in
meters. A 5.0C point charge lies at the origin and a -3.0C point charge lies at the point (3,0).
2. Find the electric potential at the points (4,0), (2,0) and (-1,0).
3. Find the x-coordinate of the point (points) on the x-axis where the potential vanishes.
4. Find the electric potential at the point (0,4).
5. On the x-axis, a point charge 3q lies at the origin and another point charge -2q lies at the point x=a. (a)
Write down an expression for the electric potential V (x ) at the point x . (b) Sketch the function V (x ) .
(c) Find the value(s) of x where the potential vanishes. (d) Find the work required to bring a third point
charge e to the point x=a/2 from infinity.
6. Point charges 4.0mC and -6.0mC lie on adjacent corners of a square of side
3.0m as shown. Find the work done by the electric field when a 3.0C point
charge moves from one unoccupied corner A to another B.
7. Find the closest distance an alpha particle (bare helium nucleus 2 He 4 ) of
kinetic energy 5.0MeV can approach a bare gold nucleus. (Atomic number of gold is 79.)
8. A proton is introduced at rest at a distance of 2  1014 m from a bare nucleus of uranium (92U238). What
is its kinetic energy in eV when it is expelled to infinity?
9. A charge of  2.00nC is uniformly distributed on a ring of radius 10.0cm that lies in the x  0 plane and
is centered at the origin. A point charge of  1.00nC is initially located on the x-axis at x  50.0cm .
Find the work required to move the point charge to the origin. (Hint: charges on the ring are equidistant
from a point on its axis.)
10. A semi-circular arc carries a uniform linear charge distribution of 5.0nC / m . Find the potential at the
center.
11. A charge of  10.0C is uniformly distributed on a thin spherical shell of radius 12.0cm. (a) What is the
magnitude of the electric field just outside and just inside the shell? (b) What is the electric potential just
outside and just inside the shell? (c) What is the electric potential and electric field at the center of the
shell? (d) What is the electric potential and electric field at a distance 24cm from the center of the shell?
12. What is the maximum potential that the dome of a van de Graaf generator can be safely charged to if its
radius is 20cm and the breakdown electric field in air is 3.0MV/m?
13. Two spherical conductors are widely separated. One has radius R and the other 2 R . Initially, the small
spheres carries a charge Q while the larger sphere is neutral. They are then connected by a long metallic
wire. What is now the charge on the small sphere?
14. A spherical conductor of radius R1 is charged to 20 kV. When it is connected by a long, very thin
conducting wire o a second conducting sphere far away, its potential drops to 12 kV. What is the radius
of the second sphere?
15. A solid sphere of radius R carries a total charge Q uniformly distributed throughout its volume. Find the
potential at a point a distance R 2 from the center.
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16. A configuration of conductors consists of a thin spherical shell of radius a , carrying a uniformly
distributed total charge Q surrounded by a concentric thick spherical shell with inner radius b and outer
radius c . Find the electric field and electric potential at a point a distance r from the center separately
for the four regions r  a, a  r  b, b  r  c, c  r when the total charge on the outer shell is (a)
zero, (b)  Q , and (c) Q .
17. How much work is required to put the two protons in place (against their mutual electric repulsion)
inside an alpha particle, assuming the distance between them is 1.0  1013 cm . Express your answer in
eV.
18. Three point charges  2.0C , 3.0C and 4.0 C lie on the vertices of an equilateral triangle of side
2.0m. How much work has been done to establish this configuration?
19. Charge is supplied to the metal dome of a Van de Graaf generator by the belt at the rate of 200μC/s
when the potential difference between the belt and the dome is 1.25MV. The dome transfers charge to
the atmosphere at the same rate, so the 1.25MV potential difference is maintained. What minimum
power is needed to drive the moving belt and maintain the 1.25 MV potential difference?
20. (Difficult)Show that the total work needed to assemble a uniformly charged sphere of total charge Q and
radius R is given by 3Q 2 200 R 
Answers
1. 4.5kV 13.5mJ
2.  15.8kV  4.5kV 38.3kV
3. 1.9m 7.5m
4. 5.9kV
3
2  3a
2ke2
3
a
5. V  ke 

a
 x xa  5
6. 26mJ
7. 4.6  1014 m
8. 6.6MeV
9. 150nJ
10. 140V
11. 6.25kV / m, 0kV / m, 750V , 750V , 1.56kV / m, 375V
12. 600kV
13. Q 3
14. R2  2R1 3
15. 11kQ 8R
16. (a) 0, kQ r 2 , 0, kQ r 2 , kQ(1 a  1 c  1 b), kQ(1 r  1 c  1 b), kQ c, kQ r
(b) 0, kQ r 2 , 0, 0, kQ(1 a  1 b) , kQ(1 r  1 b) , 0,0
(c) 0, kQ r 2 , 0, 2kQ r 2 , kQ(1 a  2 c  1 b) , kQ(1 r  2 c  1 b), 2kQ c, 2kQ r
17. 1.44MeV
18.  9mJ
19. 250W
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