Download Exam 2 Physics 195B (3/14/02)

Physics 196 Spring 2011
Name:
Exam 2
Time Allowed: 2 hours
Credits for numerical questions require evidence of calculation
Some Physics Constants:
e = 1.6×10-19 C
k = 9.0×109 Nm2/C2
ε0 = 8.85×10-12 C2/Nm2
me = 9.11×10-31 kg
mp = 1.67×10-27 kg
electronic charge
Coulomb constant
Permittivity of free space
Mass of electron
Mass of proton
PART A ( 48 points total. 3 points each.)
1. On the x-y plane, the electric field is uniform and is given by E = 500 ĵ(N / C). Find the potential difference
VB -VA between the point A , which has coordinates ( 2,-1) and B , which has coordinates ( 5, 4) where
coordinates are measured in meters.
(a)
(b)
(c)
(d)
-1500V
+1500V
-2500V
+2500V
2. The electric potential at the point A is 300V and that at the point B is -200V. Find the work done by the
electric field when a point charge of -4.0nC moves from A to B
(a)
(b)
(c)
(d)
+2.0m J
-2.0m J
+4.0m J
-4.0m J
3. A bare nucleus of an atom produces an electric potential of 720V at a distance of 5.0 ´10-11 m from it. How
many protons does the nucleus have?
(a)
(b)
(c)
(d)
10
15
20
25
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4. The velocity of an electron is 2.4 ´10 7 m / s at a point A, and becomes half as much when it reaches point B.
If only electrostatic force is present, what is the electric potential difference VB -VA between the two points?
(a)
(b)
(c)
(d)
1230V
-1230V
2460V
-2460V
5. The diagram shows a negatively charged object brought near a conductor. The points A and B are both
inside the conductor. The electric potentials there are denoted by VA and VB , After a long time, which of the
following statements is correct?
(a) VA < VB
(b) VA > VB
(c) VA = VB
(d) It depends on the total charge on the conductor
6. A lithium nucleus 3Li7 and a boron nucleus 5B10 at rest are both accelerated by the same electric potential
difference. If the final kinetic energy of the lithium nucleus is K, that of the boron nucleus is
a.
b.
c.
d.
3K/5
5K/3
7K/10
10K/7
7. The electric potential measured in volts in a region of space is given by V(x) = 4 + 5x 3 where x is in meters.
The electric field at the point x = -1 is
a. +15(V / m)iˆ
b. -15(V / m)iˆ
c. +10(V / m)iˆ
d. -10(V / m)iˆ
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8. The electric field measured in V/m in a region of space is E ( x ) = 6xiˆ where x is in meters. The potential
difference V(x=2)-V(x=1) between the points at x=2 and x=1 is
a.
b.
c.
d.
-9V
–20V
9V
20V
9. The diagram shows a number of equipotential surfaces with their potentials labeled and a point P situated at
one of the surfaces. Draw as accurately as you can a vector at P that gives the direction of the electric field.
10. What is the maximum electric potential relative to ground an isolated metallic sphere of radius 50cm can
have if the breakdown electric field strength in air is 3.0MV / m ?
(a)
(b)
(c)
(d)
2.0MV
1.5MV
1.0MV
0.5MV
11. Find the electrostatic energy of a system of four point charges occupying the corners of a square of side a as
shown:
q
-q
-q
a.
b.
c.
d.
q
-0.75kq2 / a
-1.33kq 2 / a
-2.59kq 2 / a
-3.61kq2 / a
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12. Which of the following statement(s) regarding the capacitance of a capacitor are correct?
(a)
(b)
(c)
(d)
It increases with the charge on the capacitor
It increases when the potential difference is reduced
It increases when dielectric is introduced
It increases with the size of the capacitor
13. Find the equivalent capacitance of the following combination of identical capacitors, each having a
capacitance of 3m F .
(a)
(b)
(c)
(d)
0.4m F
1.2m F
4.6m F
9.2m F
14. After a 2.00m F capacitor is charged to a potential difference of 100V , it is connected in parallel with a
second capacitor that is uncharged. The potential difference is reduced to 25V afterwards. Find the
capacitance of the second capacitor.
(a)
(b)
(c)
(d)
6.0m F
7.0m F
8.0m F
9.0m F
15. A solid spherical conductor of radius 2m has charge Q=50nC on it. A second far away spherical conductor
of radius 6m has charge 30nC. When the two are connected by a long wire, the charge on the first conductor
becomes
(a)
(b)
(c)
(d)
10nC
15nC
20nC
25nC
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16. A bare nucleus of beryllium atom 4 Be8 at rest is placed at a distance 5.0×10-10m from a potassium nucleus
which contains 19 protons. Pushed away from the electrostatic repulsion, what is the highest kinetic energy
of the beryllium nucleus?
a.
b.
c.
d.
137eV
182eV
219eV
275eV
PART B ( 52 points total)
17. On the x-y plane, a point charge -3q is at the origin, and a second point charge q is on the x-axis with
coordinate x = a .
(a) (4 points) Write expressions for the electric potential at a point on the x-axis with x-coordinate x
separately for the three regions x < 0, 0 < x < a, a < x
(b) (4 points) Sketch the potential function V ( x ) as a function of x
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(c) (4 points) Determine the x-component of the electric field E x at a point on the x-axis with coordinate
x where 0 < x < a
(d) (4 points) Write an expression for the electric potential at the point ( x, y) on the y-axis, and calculate the
x and y components of the electric field at this point.
(e) (4 points) For this part of the problem, take q = 2mC , a =1.0m . A charged particle with kinetic energy
90.0J approaches the two point charges from far away along the positive x-axis. It is found to stop at a
distance of 20cm from the positive charge. Find the charge on the particle.
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18. A conducting sphere of radius a is surrounded by a concentric conducting spherical shell of inner radius
b and outer radius c . The space between the conductors is filled with a dielectric of dielectric constant k .
The conducting sphere carries electric charge Q , and the spherical shell is neutral.
(a) (4 points) Determine the electric field at a point whose distance from the center is r separately for the
regions r > c, c > r > b, b > r > a, a > r .
(b) (4 points) Find the electric potentials of the two conductors, taking the potential to be zero at infinity.
(c) (4 points) A quantity of charge Q is now placed on the outer conductor. What is the potential difference
of the two conductors? What is the potential of the inner conductor?
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19. A parallel plate capacitors consists of two circular plates of radius 30cm separated by a distance of 1.5cm.
The plates are connected to a voltage source of 800V.
(a) (5 points) Determine the capacitance
(b) (5 points) Determine the charge and energy stored.
(c) (5 points) A piece of dielectric of dielectric constant k = 3 is now inserted into the gap between the
plates so that it fills the lower one third of the space between the gap. What is the new capacitance?
(d) (5 points) How much work is done by the external force to push the dielectric in while the plates are
connected to the voltage source? How much is it if the plates are disconnected from the source?
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