Download PHYS 196 Class Problem 1

PHYS 196 Home Work 4
1. The electric field is uniform in a region of space, being equal to 500 N/C and pointing to the east.
Consider three points A, B and C in this region. The point A is to the west of B, and the distance
between A and B is 8.0cm. The point C is north of B, and the distance between B and C is 4.0cm. Find
(a) the work done by the electric field when a point charge 3.0μC moves from A to B, (b) the potential
difference VA  VB (c) the work done by the electric field when the same charge moves from A to C, (c)
the potential difference VA  VC .
2. Find the work done against the electric field in moving an electron from A to C in the previous problem.
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3. Consider three points A,B,C on the x-y plane, where a uniform electric field E  100( N / C )iˆ exists. The
coordinates in meters for these points are: A=(4,0), B=(-1,0) and C=(-2,2). Find the potential difference
VB  VA and VC  VA .
4. At the points A and B, the potentials are 1000V and 1500V respectively.. Find (a) the electric potential
energy of a 4.0 C point charge when it is at A and at B, (b) the work done by the electric field when it
moves from A to B. (c) the work done against the electric field in the same move.
5. The uniform electric field in a region is known to be either pointing up or pointing down. The potential
at a point A in the region is 1500V, and that at a point B 4.0cm directly above A is 500V. Find the
magnitude and direction of the electric field.
6. Consider two parallel metal plates, one of which is electrically grounded while the other is held at
potential of 2.0kV. A small particle of mass 3.0mg and carrying a charge of 6.0nC is introduced woth
zero velocity at the positive plate and released. Find its kinetic energy and velocity when it reaches the
grounded plate.
7. The kinetic energy of a deuteron H 2 is 3.0MeV. Find its velocity.
8. Find the kinetic energy in eV for an electron travelling with one tenth the speed of light.
9. An aluminum ion Al 3  has been accelerated by a potential difference of 2.0kV. What is its kinetic
energy in eV, and what is its speed? (mass number of the ion is 27)
10. The picture tube of an old style TV set consists of an electron gun and a screen. The electrons from the
gun are accelerated through a potential difference of 30.0kV before striking the screen. (a) Which is at a
higher electric potential, the gun or the screen? (b) What is the kinetic energy of an electron (in eV and
in J) as it reaches the screen?
11. 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).
12. Find the electric potential at the points (4,0), (2,0) and (-1,0).
13. Find the x-coordinate of the point (points) where the potential vanishes.
14. Find the potential at the point (0,4).
15. On the x-axis, a point charge 3e lies at the origin and another point charge -2e 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.
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16. 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.
17. Find the closest distance an alpha particle of kinetic energy 5.0MeV can approach a bare gold nucleus.
(Atomic number of gold is 79.)
18. 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?
Answers
1. 120J 40V 120J 40V
2. 6.4 ´10-18 J
3. 500V 600V
4. 4mJ 6mJ  2mJ 2mJ
5. 25kN / C up
6. 12J 2.8m / s
7. 1.7  107 m / s
8. 2.6keV
9. 2.1  105 m / s
10. 30keV 4.8  1015 J
11. 4.5kV 13.5mJ
12.  15.8kV  4.5kV 38.3kV
13. 1.9m 7.5m
14. 5.9kV
3
2
15. V  ke 
 x xa
16. 26mJ
17. 4.6  1014 m
18. 6.6MeV
2
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3a
5
3a
2ke2
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