Spring 2010 Physics 212 Hour Exam 1
(24 questions)

The grading button and a description of the scoring criteria are at the bottom of this page. Basic questions are marked by a single star *. More difficult questions are marked by two stars **. The most challenging questions are marked by three stars ***.

True-false questions are worth 2 points each, three-choice multiple choice questions are worth 3 points each, five-choice multiple choice questions are worth 6 points each. The maximum possible score is 101. The exam period was 90 minutes; the mean score was 60.5; the median was 59. Click here to see page1 page2 of the formula sheet that came with the exam.


QUESTION 1**

Four equally massive charges are held in place equidistant from the origin on the x and y axes as shown in the figure. The charges on the x-axis are positive (+Q) and the charges on the y-axis are negative (-Q). When the charges are simultaneously released they

(a)   all are drawn to the origin where they collide.
(b)   all are repelled outward away from the origin.
(c)   remain fixed at their initial positions because they each experience no net force.


QUESTION 2*

Two charges are placed on the x-axis as shown in the figure. A charge of -Q is placed at the origin and a charge of +4Q is placed at x = -a.

Referring to the figure, where on the x-axis is the electric field zero?

(a)   at a point to the right of the origin
(b)   at a point between x = -a and x = 0
(c)   at a point to the left of x = -a


QUESTION 3*

This and the next question are about the following situation:

The diagram shows electric field lines (solid) and equipotential lines (dashed) for a region of space. The charges giving rise to the electric field and equipotential lines are outside of the illustrated region. The points, A, B, C and D are locations in space that are referred to in these two questions.

The magnitude of the work done by an external agent in moving a positive test charge from point C to point D is

(a)   less than the magnitude of the work done to move the same positive charge from point A to point B.
(b)   more than the magnitude of the work done to move the same positive charge from point A to point B.
(c)   equal to the magnitude of the work done to move the same positive charge from point A to point B.


QUESTION 4*

The electric potential is greater at B than at D.

(T)   True
(F)   False


QUESTION 5**

Two infinite line charges of equal magnitude λ but opposite sign are fixed in the x-y plane, parallel to the y-axis. The line charges intersect the x-axis at ±a as shown in the figure.

The electric field at the orgin is

(a)   
(b)   
(c)   
(d)   
(e)   


QUESTION 6***

A conducting spherical shell of inner radius a and outer radius b has a positive net charge Q.

Which one of the above graphs best represents the magnitude of the electric potential as a function of radial distance from the center of the shell?

(a)   
(b)   
(c)   


QUESTION 7**

A capacitor C1 is charged by being attached to a battery having voltage V. After it is charged, C1 is disconnected from the battery. Assume that the battery charges capacitor C1 to total charge Q.

Charged capacitor C1 is now connected to uncharged capacitor C2 as shown. Which statement below is valid about the voltage V1 across capacitor C1 after being connected to capacitor C2?

(a)   Charge is conserved, so the charge on both capacitors is the same as the original charge on capacitor C1. Since V = Q/C, the voltage V1 must be the same as the original voltage V.

(b)   The original charge on C1 redistributes, so the charge on C1 is less than before. Therefore, V1 has to be less than V after being connected to C2.

(c)   The two capacitors are connected in parallel, so they must have the same voltage, and the only voltage they can share is V. Therefore, the voltage across C1 after being connected to C2 is V, the original battery voltage.


QUESTION 8***

Capacitor C1 is again charged to total charge Q, disconnected from the battery, and then connected to two other capacitors (initially uncharged) as shown. The capacitances are related as follows: C2 = (1/2)C1 and C3 = 2C1. What is the final charge on capacitor C2 in terms of Q? (Hint: think carefully about how the three capacitors are connected. Recall: this question asks about the charge on C2.)

(a)   (1/3) Q
(b)   (1/7) Q
(c)   (1/5) Q
(d)   (3/14) Q
(e)   (5/7) Q


QUESTION 9*

This and the next three questions are about the following situation:

An infinite conducting metal plate with thickness T is parallel to an infinite sheet of charge with a surface charge density σ. The distance between the center of the metal plate and sheet of charge is d. The field between the sheet of charge and the metal plate is E = ELx and the field to the right of the metal plate is E = ERx. Assume that ER > 0 and ER > 0, as shown in the figure; EL and ER may not be equal in magnitude. The surface charge density on the left and right surfaces of the metal plate are denoted σL and σR respectively. No other charges are present. It is not known if there is a net charge on the conducting plate.

Which one of these expressions correctly describes the voltage difference ΔV = Vsheet - Vplate?

(a)   
(b)   
(c)   
(d)   
(e)   


QUESTION 10*

If EL = ER, the total charge on the metal plate is zero?

(T)   True
(F)   False


QUESTION 11*

Which statement correctly summarizes the relationship between σL and σR ?

(a)   σL and σR are of the opposite sign.
(b)   σL and σR are of the same sign.
(c)   σL and σR are always equal.


QUESTION 12***

The charge density on the infinite sheet of charge σ can be computed in terms of EL and ER. Which is the correct expression for σ ?

(a)   σ = ε0(ER-EL) / 2
(b)   σ = -2ε0(ER+EL)
(c)   σ = ε0(ER+EL)
(d)   σ = 2ε0(ER+EL)
(e)   σ = ε0(EL-ER) / 2


QUESTION 13**

This and the next three questions are about the following situation:

The figure shows a cross-sectional view of two concentric, infinite length, conducting cylindrical shells. The inner shell has as an inner radius of a and an outer radius of b. The electric field just outside the inner shell has magnitude E0 and points radially outward as shown. The grounded, outer shell has an inner radius c and an outer radius of d.

Some of the cylindrical surfaces may be charged. Let σa, σb, σc and σd be the surface charge densities on the surfaces with radii a, b, c and d. There are no other charges or conductors in the problem.

The surface charge density σa is zero.

(T)   True
(F)   False


QUESTION 14**

Which expression correctly gives the potential, V, of the inner conducting shell?

(a)   
(b)   
(c)   
(d)   
(e)   


QUESTION 15**

Which statement correctly compares |σc| and |σd| ?

(a)   |σc| = |σd|
(b)   |σc| > |σd|
(c)   |σc| < |σd|


QUESTION 16***

Which expression is the correct expression for σc ?

(a)   σc = 2ε0E0
(b)   σc = -ε0E0
(c)   σc = +ε0E0(c/d)
(d)   σc = ε0E0
(e)   σc = -ε0E0(b/c)


QUESTION 17***

Parallel plate capacitor #1 has plate area A, separation distance d, and capacitance C1. Parallel plate capacitor #2 is made by starting with capacitor #1 and adding a dielectric with k = 2 of thickness d/2 that covers half the area Adielectric = (1/2)A. What is the capacitance C2 of capacitor #2 in terms of C1.

(a)   
(b)   
(c)   
(d)   
(e)   


QUESTION 18**

Two identical dielectrics with κ > 1 are inserted into two identical capacitors in two different ways as follows:
1) The first capacitor is charged from a battery, disconnected, and then the dielectric is inserted so that it is totally between the plates.

2) The second capacitor remains connected to the same battery and then the dielectric is inserted so that it is totally between the plates.

After the dielectrics are inserted in both cases:

(a)   The energy stored in the first capacitor in case 1) is larger than the energy stored in the second capacitor in case 2).

(b)   The energy stored in the first capacitor in case 1) is smaller than the energy stored in the second capacitor in case 2).

(c)   The energy stored in both capacitors is the same.


QUESTION 19*

Two charges, +Q and -Q (equal in magnitude but opposite in sign) are fixed at a distance a from the origin on the x-axis. Point P is located at a distance b from the origin on the y-axis.

Now, a charge, q = +1 μC, is brought in from infinity and placed at point P. The total potential energy of the charge collection

(a)   increases, because positive net work was done on q bringing it in from infinity.
(b)   remains unchanged, because no net work was done on q bringing it in from infinity.
(c)   decreases, because negative net work was done on q bringing it in from infinity.


QUESTION 20*

This and the next two questions are about the following situation:

Three charges Q1, Q2 and Q3 are arranged on the y-axis as shown in the figure below. A fourth charge q is brought in from infinity, and placed on the x-axis a distance of a = 1 m from the origin. Q1 is located at (0, a), Q2 is located at the origin and Q3 is located at (0,-a).

Find the energy stored in the charge configuration of Q1, Q2 and Q3 (the work which was necessary to assemble the three charges in the absence of q).

(a)   U = -0.201 J
(b)   U = -0.0123 J
(c)   U = 0.00475 J
(d)   U = 0.0345 J
(e)   U = 0.0693 J


QUESTION 21*

Find the x-component of the net force by Q1, Q2 and Q3 on q.

(a)   Fx = -0.0378 N
(b)   Fx = -0.0252 N
(c)   Fx = 0.0180 N
(d)   Fx = 0.0334 N
(e)   Fx = 0.0524 N


QUESTION 22**

An external agent must do positive work in order to bring q in from infinity.

(T)   True
(F)   False


QUESTION 23**

This and the next question are about the following situation:

A negative test charge of mass m and charge -q is placed a distance z above the center of a uniformly, positively charged circular hoop of radius b, with a linear charge density of λ C/m.


Which of these graphs best represents the potential energy U of the negative test charge as a function of z, assuming λ > 0 ?

(a)   
(b)   
(c)   
(d)   
(e)   


QUESTION 24***

If the negative test charge is released from rest at z = b, which expression correctly expresses the maximum speed of the test charge assuming λ > 0 ?

(a)   
(b)   
(c)   
(d)   
(e)