Physics 2B Sample Midterm Exam #1
(49 points)
by Todd Sauke
(Actual Midterm will be shorter than this.)
Question #1. (6 pts)
A point charge Q = -800 nC (nanoCoulombs) and two unknown point charges,
q1 and q2, are placed as shown in the figure
at right. The electric field at the origin O,
due to charges Q, q1 and q2, is equal to zero.
We want to determine the values of charges
q1 and q2. The electric field vector at the
origin has two components (x and y).
Because the electric field at the origin is
zero, both the x and y components are zero.
We can consider the x and y components
separately. Remember that the y component
of the electric field at the origin due to q1 is
zero, since it is on the x axis. What is the y
component of the E field at the origin due to
the charge Q? (Use a trigonometric function
to obtain the y component.)
_______________________________ N/C
1 point (check the sign!)
What must be the y component of the E field at the origin due to q2 (in order to cancel out the E
field from Q)?
________________________________N/C
1 point
What must the charge q2 be to provide this field?
_________________________________nC
1 point
(note units!)
Working similarly, what must the charge q1 be in order for the E field at the origin to be zero?
_________________________________nC
2 points
How many excess electrons are there in the charge Q?
_________________________________
1 point
Question #2. (3 pts.)
As shown in the figure above, a circular plate with radius 1.96 m contains 793 μC (microCoulombs) of a charge uniformly distributed. We want to find the magnitude of the electric field
near the plate. First, what is the charge density, σ, of the given charge distribution?
_________________________________C/m2
1 point
Now, write the equation from the study guide that relates the field near a sheet of charge to the
charge density, σ.
______________________________
1 point
What is the magnitude of the electric field near the plate?
_______________________________
1 point
Question #3.
(2 points)
In the figure at right, charge is placed on an
irregularly shaped piece of copper, a good
electrical conductor. How will the charge be
distributed on the object?
A)
B)
C)
D)
E)
With greatest density neat point E on the flat surface.
With greatest density near point C on the surface.
With gratest density near point D in the interior.
Uniformly throughout the volume.
Uniformly over the surface.
Question #4. (5 pts.)
A nonuniform electric field is directed along the x-axis at all points in space. The magnitude of
the field varies with x, but not with respect to y or z. The axis of a cylindrical surface, 0.80 m
long and 0.20 m in diameter, is aligned parallel to the x-axis. The electric fields E1 and E2, at the
ends of the cylindrical surface, have magnitudes of 3000 N/C and 7000 N/C respectively, and are
directed as shown in the figure above. What is the electric flux exiting the cylinder's circular
surface at the left end?
_____________________________N m2/C
1 point (check your signs)
What is the electric flux exiting the cylinder's circular surface at the right end?
_____________________________N m2/C
1 point (check your signs)
What is the angle between the electric field and the side surface of the cylinder?
______________________________radians
½ point
What is the electric flux exiting this side surface?
______________________________
½ point
Write the equation relating the total flux exiting a closed surface to the total charge enclosed
within that surface.
______________________________________
1 point
What is the charge enclosed by the cylinder?
(check your sign!)
___________________________
______
1 point
(include units for full credit)
Question #5. (5 pts.)
Point charges, Q1 = +58 nC and Q2 = -90
nC, are placed as shown in the figure at
right. An electron is released from rest at
point C. (The electron will experience a
force to the right, and accelerate in that
direction.) We want to find the speed of the
electron as it approaches infinity (far away).
The force on the electron changes as it
moves away, so we can't use constant
acceleration equations.
Instead let's use the concept of potential energy, together with the Work-Energy theorem. Taking the
potential energy of the electron to be zero when it is at infinity (far away), write the equation from the
study guide that gives the potential energy of the electron at point C.
_____________________________________
1 point
What is the potential energy of the electron at point C?
______________________________
1 point
What is the equation relating the potential energy and the kinetic energy of the electron at t = 0 and at t
= ∞ (when the electron is far away)?
____________________________________
1 point
What is the speed of the electron when it approaches infinity (far away)?
__________________________________ ______
2 points
(include units to get full credit)
Question #6.
(2 points)
Two conductors are joined by a long copper wire. Thus
A) each carries the same free charge.
B) the potential on the wire is the average of the potential of each conductor.
C) the electric field at the surface of each conductor is the same.
D) no free charge can be present on either conductor.
E) each conductor must be at the same potential.
Question #7. (6 pts.) The voltage and power ratings of a light bulb, which are the normal operating
values, are 110 V and 40 W. Assume the filament resistance of the bulb is constant and has a value, R,
independent of operating conditions.
The light bulb is operated at a reduced voltage, VRed, and the power drawn by the bulb is 25 W.
Write the TWO equations relating power, voltage, and resistance for the two cases under consideration
(the normal, full-power case, and the special, reduced-voltage case).
______________________________
1 points
_________________________________
1 points
You should have TWO equations and TWO unknowns. What are the TWO unknowns?
___________
0.5 points
___________
0.5 points
Solve the two equations for the unknown reduced operating voltage VRed.
The operating voltage of the bulb is:
_________________________
3 points
_______________________________________________________________________________________
Question #8. (4 pts.) Given the same situation as Question #7 above, i.e. a 40 W light bulb, the light
bulb is operated with a current which is one half of the current rating of the bulb (one half of the normal
current).
Write the equation for the reduced electrical power, PRed, as a function of reduced voltage and current
(VRed, and IRed).
_______________________
½ point
Write the equation for the reduced voltage, VRed, across the resistance of the light bulb as a function of
the resistance, R, and the current, IRed, through it.
_______________________
½ point
Plug this second equation into the first to obtain a third equation, (eliminating VRed ), and relating the
reduced power to the reduced current, IRed, and the resistance, R.
________________________
1 point
The actual power, PRed, drawn by the bulb is:
________________________
2 points
Question #9. (6 pts.) The emf and the internal resistance of a battery are 31 Volts and 2 Ohms,
respectively. Draw a figure below showing the equivalent circuit for this battery. Label the positive
terminal "a" and the negative terminal "b".
1 point
Write an equation for the voltage across the internal resistance.
___________________________
1 points
When the terminal voltage, Vab is equal to 17.4 V, the current through the battery, including direction, is:
________________ Ohms
(Circle direction at right:)
2 points
Volts (Circle one unit at left, 1 point)
Amps
Volts per meter
from (a to b)
OR
from (b to a)
1 points
_______________________________________________________________________________________
Question #10. (4 pts.) A wire of radius 1.1 mm carries a current of 2.5 A. The potential difference
between points on the wire 49 m apart is 2.6 V. Write the equation relating the electric field in the wire
to the voltage mentioned in the problem.
______________________________
½ point
What is the electric field in the wire?
________________________________ V / m
1 points
Write the equation relating the resistivity of the material of which the wire is made to the resistance, R,
of the wire (between the 49 meters separated points) and to the other quantities mentioned in the
problem.
____________________________________________
½ point
What is the resistance of the wire (between the 49 meters separated points)?
_________________
1 point
What is the resistivity, ρ , of the material of which the wire is made?
_____________________________________________ Ω m 1 points
Question #11. (6 pts.) A resistor with resistance 470 Ω is in a series with a capacitor of capacitance
8.5 x 10-6 F. We want to determine what capacitance must be placed in parallel with the original
capacitance to change the capacitive time constant of the combination to three times its original value.
Write an equation for the equivalent capacitance, Ceq, of the parallel combination of the given
capacitor, C, and the unknown capacitor, Cu.
______________________________
1 point
Write an equation for the original capacitive time constant, τ0, in terms of the resistance and the given
capacitance, C.
______________________________
1 point
Write an equation for the capacitive time constant, τ, in terms of the resistance and the equivalent
capacitance of the parallel capacitors, Ceq.
______________________________
1 point
We have these THREE equations. We are told that we want to consider the case for which the time
constant, τ, is three times it's original value, τ0. (τ = 3 τ0) This is a FOURTH equation.
What are the FOUR unknowns?
τ
τ0
__________ _________
(given)
(given)
________________
0.5 points
_____________
0.5 points
Four equations with four unknowns may seem "hard" or "scary". Of course you should see, however, that this is an easy
problem. Most of the equations (like τ = 3 τ0 ) are so easy that normally we wouldn't even count it as an equation (and we
wouldn't count τ0 as an unknown). We just plug in the values as we go along with our "real" equations, making substitutions
for some unknowns in terms of others for which we have "easy" equations. (A confident, capable, person could actually just
write down a single equation, (the one given τ = 3 τ0) and just plug in the values corresponding to the three equations
asked for above from their head while writing it all down, keeping only the single unknown, Cu , and solving the one
equation with the one unknown.) Solve the equations for the unknown capacitance, Cu , which must be
placed in parallel with the original capacitance to change the capacitive time constant of the
combination to three times its original value.
Cu = ____________________
2 points