Physics 212 Exam I Sample Question Bank 2006

Physics 212
Exam I Sample Question Bank
Multiple Choice: choose the best answer
"none of the above" may can be a valid answer
2006
___ The (attempted) demonstration in class with the pith balls and a variety of materials indicated that
(A) there are two kinds of electrical properties (now referred to as positive and negative charge).
(B) objects with the same type of charge repel, while objects with different types of charge attract.
(C) "charge is conserved" in that whenever a positive charge is produced, an equal amount of negative is
also produced.
(D) all of the above.
(E) electric charge was never discussed in this class.
___ . A rod with an unknown charge attracts a pith ball (as in the attempted lecture demonstration). Which of
the following could describe the situation?
(A) The rod has negative charge and the pith ball has positive charge.
(B) The rod has positive charge and the pith ball has negative charge.
(C) They both have positive charge.
(D) They both have negative charge.
(E) Both A and B above.
___ . The lab exercise with scotch tape and a variety of other materials indicated that
(A) there are two kinds of electrical properties (now referred to as positive and negative charge).
(B) objects with the same type of charge repel, while objects with different types of charge attract.
(C) "charge is conserved" in that whenever a positive charge is produced, an equal amount of negative is
also produced.
(D) all of the above.
(E) none of the above.
___ The lab exercise with scotch tape and a variety of other materials indicated that
(A) there are three kinds of electrical properties (now referred to as positive, negative and magnetic
charge).
(B) objects with the same type of charge attract, while objects with different types of charge repel.
(C) "charge is quantized " in that on average, the charge created is an integer multiple of the neutron’s
charge.
(D) all of the above.
(E) none of the above.
___ . Total electric charge in a closed system is conserved
(A) always.
(B) never.
(C) only in conductors.
(D) except within conductors.
(E) electric charge conservation was never discussed in this class.
___ . An electron has negative charge
(A) as a consequence of the conventions set by Benjamin Franklin.
(B) means that the electric force on the electron and the electric field are in opposite directions.
(C) results in an attractive force between the electrons and the positively charged protons in an atom's
nucleus.
(D) all of the above.
1
(E) none of the above.
Physics 212
Exam I Sample Question Bank
2006
___ . An electron has negative charge
(A) as a consequence of the conventions set by Thomas Jefferson.
(B) means that the electric force on the electron and the electric field are in opposite
directions.
(C) results in an repulsive force between the electrons and the positively charged
protons in an atom's nucleus.
(D) all of the above.
(E) none of the above.
___ . An electron has positive charge
(A) as a consequence of the conventions set by Benjamin Franklin.
(B) means that the electric force on the electron and the electric field are in opposite directions.
(C) results in an attractive force between the electrons and the positively charged protons in an atom's
nucleus.
(D) all of the above.
(E) trick question, an electron is has negative charge.
___ Relative to the gravitational attraction between two protons, the electrostatic repulsion is
(A) much larger.
(B) about the same.
(C) much smaller.
(D) trick question since the gravitational force will be repulsive, not attractive.
(E) zero between the same kinds of particles.
___ The electrostatic repulsion between two electrons is
(A) much greater than the gravitational attraction between the electrons.
(B) about the same as the gravitational attraction between the electrons.
(C) much less than the gravitational attraction between the electrons.
(D) the answer to this depends upon the actual separation between the electrons.
(E) trick question since there is no gravitational attraction between electrons.
___. As two positive charges are brought closer together
(A) the repulsive force between them will decrease in magnitude.
(B) the repulsive force between them will increase in magnitude.
(C) the attractive force between them will decrease in magnitude.
(D) the attractive force between them will increase in magnitude.
(E) trick question since the force does not depend upon the separation between the charges.
___ . Two identical charges repel each other with a force of 16N. If the distance between the charges is
doubled, the force will be
(A)
1N.
(B)
2N.
(C)
8N.
(D)
16N.
(E)
none of the above.
Physics 212
Exam I Sample Question Bank
2006
___ . Two identical charges repel each other with a force of 4N. If the distance between the charges is halved,
the force will be
(A) 1N.
(B) 2N.
(C) 8N.
(D) 16N.
(E) none of the above.
___ . A positive charge of 4.0 µC exerts an attractive force of 8N on an unknown charge 20 cm away. The
unknown charge is
(A)
+ 8.9 µC .
(B)
- 8.9 µC .
(C)
+ 44. µC .
(D)
- 44. µC .
(E)
none of the above.
___ . What must be the charge of a particle of mass 1kg for it to be levitated in a 1000 N/C downward directed
electric field?
(A) + 9.8 µC.
(B) - 9.8 µC.
(C) + 9.8 nC.
(D) - 9.8 nC.
(E) none of the above.
___ . In a static situation, if there is excess charge on a conductor then
(A) the charge lies only on the surface of the conductor.
(B) the charge is in constant motion throughout the conductor.
(C) the charge evaporates from the conductor until there is no more excess charge.
(D) the charge lies at the geometric center of the conductor.
(E) the conductor explodes violently.
___ . A conductor is a material in which, under static conditions,
(A) there are charges which are free to move.
(B) the electric field is always zero.
(C) the electric potential is always constant.
(D) all of the above.
(E) none of the above.
___ . A conductor is a material in which, under static conditions,
(A) there are charges which are free to move.
(B) the electric field is always zero.
(C) the electric potential is same throughout.
(D) all of the above.
(E) none of the above.
Physics 212
Exam I Sample Question Bank
2006
___ . A rectangular area is oriented in a uniform Electric field directed left to right in the geometries shown
below. Which geometry results in the greatest electric flux through the area?
(A)
A
(B)
A
E
E
A
A
(C)
(D)
E
E
(E) the flux is the same in all these cases..
___ . A perfectly cubical gaussian surface has a point charge of Q exactly at its geometric
center. The Electric flux through one of the six faces of the cube is
(A)
Q/εo.
(B)
Q/2εo.
(C)
Q/6εo.
(D)
0.
(E)
much more information is necessary to answer.
____ . A perfectly cubical gaussian surface has an electric dipole (two charges (±Q ) of equal
size put opposite signs separated by a distance l ) at its geometric center. The total
Electric flux through all of the six faces of the cube is
(A) 2Q/εo.
(B) Q/2εo.
(C) Q/3εo.
(D) 0.
(E) much more information is necessary to answer.
___ . A perfectly spherical gaussian surface has a point charge of Q exactly at its geometric
center. The electric flux through the bottom hemisphere (half-sphere) of the gaussian
surface is
(A)
Q/εo.
(B)
Q/2εo.
(C)
Q/6εo.
(D)
0.
(E)
much more information is necessary to answer.
Physics 212
Exam I Sample Question Bank
2006
___ . A perfectly spherical gaussian surface has a an electric dipole (two charges (±Q ) of equal
size but opposite signs separated by a distance l ) at its geometric center. The total
Electric flux through the gaussian surface is
(A)
Q/εo.
(B)
Q/2εo.
(C)
Q/6εo.
(D)
0.
(E)
much more information is necessary to answer.
___. A perfectly cubical gaussian surface has a point charge of Q exactly at its geometric center. The Electric
flux through one of the six faces of the cube is
(A)
Q/εo.
(B)
Q/2εo.
(C)
Q/6εo.
(D)
0.
(E)
much more information is necessary to answer.
___. The electric field lines at a certain location
(A) are parallel to the electric force on a test charge placed at that location.
(B) are to perpendicular lines (surfaces) of constant electric potential at that location.
(C) never cross.
(D) start on positive charges and end on negative charges.
(E) all of the above.
___ . The electric field lines at a certain location
(A) only cross at the location of magnetic monopoles.
(B) are parallel to the electric force on a test charge placed at that location.
(C) are parallel to lines (surfaces) of constant electric potential at that location.
(D) start on positive charges and end on negative charges.
(E) all of the above.
___ . The electric field lines at a certain location
(A)
never cross.
(B)
are parallel to the electric force on a test charge placed at that location.
(C)
are perpendicular to lines (surfaces) of constant electric potential at that location.
(D)
start on positive charges and end on negative charges.
(E)
all of the above.
___. Gauss's law
(A) relates the total electric flux through a closed surface with the net electric charge enclosed within the
surface.
(B) is completely equivalent to the inverse square law for the electric field due to a point charge.
(C) implies that in static situations any excess charge on a conductor must lie on its surface.
(D) is very useful for charge configurations with symmetry.
(E) all of the above.
Physics 212
Exam I Sample Question Bank
2006
___ . Gauss's law tells us that
(A) if the net charge within a spherical surface is zero, then the electric field is zero.
(B) if the electric flux through a spherical surface is zero, then there is no charge within the
sphere.
(C) if the electric flux through a spherical surface is zero, then the net charge within the
sphere is zero.
(D) Coulomb's law is wrong.
(E) we can know absolutely nothing about charge contained within a spherical surface.
___ . In a static situation, if there is excess charge on a conductor then
(A) the charge lies only on the surface of the conductor.
(B) the charge is in constant motion throughout the conductor.
(C) the charge evaporates from the conductor until there is no more excess charge.
(D) the charge lies at the geometric center of the conductor.
(E) the conductor explodes violently.
___ . Identify the most correct statement
(A) Gauss’s law is equivalent to Coulomb’s law.
(B) Coulomb’s law is equivalent to Gauss’s law.
(C) Gauss’s law is equivalent to Coulomb’s law only in situations with symmetry.
(D) both (A) and (B).
(E) Gauss’s law and Coulomb’s law are completely unrelated.
___ . The electric field has magnitude 1000 N/C between parallel conducting plates separated by 5 mm (.005m).
The potential difference between the plates is
(A) 5V
(B) 200V.
(C) 5,000V.
(D) 200,000V.
(E) none of the above.
___. The electric field is directed
(A) away from areas with low electrical potential towards areas with higher electrical potential.
(B) away from areas with high electrical potential towards areas with lower electrical potential.
(C) along paths of constant electric potential.
(D) along spirals.
(E) electric fields are scalar quantities, and thus have no direction associated with them.
___. The electric field magnitude near (but outside of) an irregularly shaped conductor
(A) will be greatest where the surface has the sharpest curvature.
(B) will be greatest where the surface has the flattest curvature.
(C) does not depend upon the shape of the conductor.
(D) will necessarily be zero.
(E) trick question; since the electric field is a scalar quantity, the term “electric field magnitude” is
meaningless.
Physics 212
Exam I Sample Question Bank
___ . The electric potential is
(A) is potential energy per unit charge.
(B) is electrical force per unit charge.
(C) is simply electrical energy.
(D) is simply electrical charge.
(E) always zero within conductors.
___ . The electric potential is
(A) is simply electrical energy.
(B) is simply electrical charge.
(C) is potential energy per unit charge.
(D) is electrical force per unit charge.
(E) always zero within conductors.
2006
Physics 212
Short Questions
Exam I Sample Question Bank
2006
What are the qualitative similarities and differences between Coulomb's Law and Newton's Law of Universal
Gravitation. (be brief and specific)
Describe what happens to an uncharged conductor when a positive charge is brought near. Explain any forces
that are exerted on the conductor. A sketch or drawing may be helpful.
Describe what happens to an uncharged insulator when a positive charge is brought near. Explain any (net)
forces that are exerted on the insulator. A sketch or drawing may be helpful.
Draw the electric field lines for the two conductors below (the total charges on each conductor are the equal but
opposite)
+
−
−
−
−
−
Draw the electric field lines for the two conductors below (the total charges on each conductor are the equal but
opposite)
+
+
+
+
+
−
−
−
−
−
Draw the electric field lines for the charge configuration below (the total charges on each object are the same
and both are positive)
+
+
Physics 212
Exam I Sample Question Bank
Problems: Show all work. No work = no credit!
Three source charges are placed as
shown. Q1 is located at (0,4m) and has a
charge of +81µC. Q2 is located at (0,0)
and has a charge of +125µC. Q3 is
located at (3m, 0) and has a charge of −
64µC.
a) Calculate the Electric Field (x and y
components) at the point (3m, 4m).
b) Calculate the electric potential at the
point (3m, 4m).
A test charge of 30 µC is placed at the
point (3m, 4m).
2006
Q1
Q2
Q3
c) What is the force on this charge?
d) What is its (electrostatic) potential
energy?
A +200 µC charge (Q1) is placed at x = 0 m, y = 2 m. A −200µC charge (Q2) is placed (2m,2m)). A charge of
+400µC charge (q) is located at (2m,2m).
(A) What are the components of the electric field at the location of q due to the other two charges ? (q will
effectively be the "test charge")
(B) What are the components the force on q?
(C) What is the electrostatic potential at the location of q due to the other two charges ?
(D) What is the potential energy of q due to the presence of the other two charges?
Q1
q
Q
2
Physics 212
Exam I Sample Question Bank
Three charges are placed as shown at right,
Q1 = −64 µC at (0,3m),
Q2 = 125 µC at (0,0), and
Q3 = 27 µC at (4m,0),
(A) Determine the x and y components of the
electric field at the location (4m,3m).
(B) Determine the x and y components of electric
force on a charge q = 30 µC placed at the point
(4m,3m).
2006
Q1
3m
4m
Q3
Q2
Three source charges are placed at the
corners of an equilateral triangle 2m on a
side, as shown. Q1 and Q2 are located on
the base corners, and have a charge of
+10µC each. Q2 is located at top corner
and has a charge of -10µC. a) Calculate
the Electric Field (x and y components)
at the point at the center of the triangle.
b) Calculate the electric potential at the
point at the center of the triangle.
Q3
A test charge of 30 µC is placed at the
point at the center of the triangle.
c) What is the force on this charge?
d) What is its (electrostatic) potential
energy?
Q1
Q2
An electron gun accelerates electrons across a potential difference of 30.0 kV. The beam is fired horizontally
between to charged conducting plates in order to deflect the beam vertically. The deflecting plates are 2.00 cm
long, separated by 1.00 cm and have a potential difference of 2.00kV.
a) What is the speed of the electrons as they leave the accelerating potential?
b) What is the electric field between the deflecting plates?
c) What is the electric force on the electrons?
d) How long are the electrons between the plates? (time, in seconds)
e) What is the vertical component of velocity as the electrons leave the deflecting plates?
f) What is the final direction of the electron beam? (i.e. direction of final electron velocity)
Physics 212
Exam I Sample Question Bank
2006
A proton (q=+e, m=1.66x10-27kg) is accelerated from rest across a potential difference of 20kV.
a) What is the kinetic energy (in electron volts) of the proton as it leaves the accelerator?
b) What is this energy in Joules?
c) What is the speed of the proton ?
The proton now reaches a region with a uniform electric field produced by parallel conducting plates
separated by 1cm with a potential difference of 2000V between them, producing a upward directed electric field
which extends 5 cm in the horizontal direction.
d) What is the electric field magnitude in the region between the plates?
e) How long is the proton in this region?
f) What is the acceleration of the proton while in this region?
g) What are the x and y components of velocity of the proton as it leaves the region?
5 cm
"proton" gun
p
E
A line of charge Q lies on the y axis and extends from −a. to +a. (total length of 2a ). We wish to derive an
expression for the electric field for a point on the x-axis. From the symmetry of the configuration, the net
Electric field along the x-axis should only have an x component. A typical point is indicated on the diagram
below. We will consider the contributions of each (infinitesimal) section of the line of charge of where the
length of the segment is dy.
a) Determine the charge per unit length λ .
b) Determine the charge of a piece of length dy.
(for c-f express all geometric factors in terms of x and y only!)
c) Determine the distance from the piece of charge to the field point.
d) Determine the magnitude of the electric field due to this piece.
e) Determine the x component of the electric field due to this piece.
f) Since the contribution to the x component of the electric field will be the same for every such section of the
ring, set up but do not evaluate the integral which will add up all such components to find the net component of
the electric (i.e. add up all contributions along the axis, dy at a time, to account for the length of charge).
+a
dy
y
P
Ex
x
E
−a
Physics 212
Exam I Sample Question Bank
2006
Two oppositely charged point charges +/- q lie on the y axis at +a and -a as shown. Express ALL answers in
terms of x, a, q and k.
+q
a) What is the magnitude of the electric field
y=a
contribution from the top charge?
Indicate the direction of this contribution
a
on the diagram.
c) What is the x-component of this contribution to
the electreic field?
d) What is the y-component of this contribution to
x
the electreic field?
e) What is the magnitude of the electric field
field
contribution from the bottom charge?
point
Indicate the direction of this contribution
on the diagram.
f) Indicate the direction of this contribution on the -q
y=-a
diagram below.
g) What is the x-component of this contribution
to the electreic field?
h) What is the y-component of this contribution to
the electreic field?
i) What is the net x-component?
j) What is the net y-component?
k) sketch a graph of the net y component
A ring of of charge Q lies in the y-z plane and has a radius of a. We wish to derive an expression for the
electric field for a point on the x-axis. From the symetry of the configuration, the net Electric field along the x
axis should only have an x component. A typical point is indicated on the diagram below. We will consider the
contributions of each (infinitesimal) section of the ring of charge of where the length of the segment is ds.
a) What is the charge per unit length λ?
b) What is the charge of a piece of length ds.
(for c-e express all geometric factors in terms of x and a only!)
c) What is the distance from the piece of charge to the field point?
d) What is the magnitude of the electric field due to this piece?
e) What is the x component of the electric field due to this piece?
f) Since the contribution to the x component of the electric field will be the same for every such section of the
ring, by inspection add up all such components to find the net component of the electric (i.e. add up all
contributions along ds to account for the entire circumference of the ring).
ds
a
P
x
Ex
E
Physics 212
Exam I Sample Question Bank
2006
A long coaxial cable consists of an inner cylindrical conductor with a radius a and
an outer concentric cylinder with inner radius b and outer radius c. The inner
cylinder has a charge per unit length λ, and the outer cylinder has no net charge.
(A) Give an expression for the electric field magnitude in terms of the distance r
from the center of the spheres for the following regions:
r<a
a<r<b
b<r<c
c< r
(B) Draw a graph of the electric field magnitude for 0 < r < 2c
(C) What is the charge per unit length on the inner surface of the hollow sphere?
(D) What is the charge per unit length on the outer surface of the hollow sphere?
a
q
b
q
c
q
E(r)
a
A solid conducting sphere of radius a carries a charge q. It is inside a concentric hollow
conducting sphere of inner radius b and outer radius c. The outer sphere carries a net
charge of –q.
(A) Give an expression for the electric field in terms of the distance r from the center of
the spheres for the following regions:
r<a
a<r<b
b<r<c
c<r
E(r)
(B) Draw a graph of the electric field magnitude for 0 < r < 2c
(C) What is the charge on the inner surface of the hollow field?
(D) What is the charge on the outer surface of the hollow field?
(E) Using your expression for E(r) for the region a < r < b , determine
Vab by evaluating the final term in
b
  b
Vab = ∫ E ⋅ dl = ∫ E ( r ) dr
a
a
a
b
b
c
r
q
a b
c
r
c
Physics 212
Exam I Sample Question Bank
An infinitely long solid conducting cylinder of radius a carries a charge per
unit length λ. It is inside a concentric hollow conducting cylinder of inner
radius b and outer radius c. The outer cylinder carries a net charge per unit
length of –λ.
(A) Give an expression for the electric field in terms of the distance r from the
center of the cylinder for the following regions:
r<a
a<r<b
b<r<c
c<r
2006
a
b
c
E(r)
(B) Draw a graph of the electric field magnitude for 0 < r < 2c
(C) What is the charge on the inner surface of the hollow field?
(D) What is the charge on the outer surface of the hollow field?
(E) Using your expression for E(r) for the region a < r < b , determine
Vab by evaluating the final term in
b
  b
Vab = ∫ E ⋅ dl = ∫ E ( r ) dr
a
r
a
b
c
a
An proton is accelerated from rest across a potential difference of 10 million Volts.
a) What is the kinetic energy (in Joules) of the proton as it leaves the accelerator?
b) What is the speed of the proton?
The proton now makes a head on “collision” (approaching from “very far away”) with a gold nucleus
(which has atomic number 79, and hence a charge of +79e). Assume the nucleus is stationary for this
problem.
c)
d)
e)
f)
What is the speed of the proton at the turn around point?
What is the kinetic energy of the proton at the turn around point?
What is the potential energy of the proton at the turn around point?
What is the distance between the proton and the nucleus at the turn around point?
proton
proton accelerator
+e
+79e
gold nucleus