Department of PhysicsUniversity of California, San Diego

Physics 2B – Summer Session I, 2014Instructor: Brian Shotwell

Practice Midterm 1.1, TEST FORM xxJuly 10, 2014

Reminder: make sure you do the following or you will be penalized up to 20% on this test:

• Write down AND bubble in your 3-digit exam code number under “EXAM NUMBER.”• Do NOT write or bubble in anything under “ID NUMBER.”• Bubble in the “TEST FORM” (A-D) that appears at the top of your midterm/final.• Write your name on your scantron.• Turn in your scantron to the correct pile (A-D).• Use the correct scantron form: X-101864-PAR-L. Use a pencil!

1. Which of the following statements most accurately sums up Gauss’s Law?

A) The electric potential inside a closed surface is proportional to the net charge inside the surface.B) The electric potential energy inside a closed surface is proportional to the net charge inside the surface.C) The net electric flux through any closed surface is proportional to the net charge inside the surface.D) The net electric flux inside a closed surface is proportional to the net charge inside the surface.E) The electric field inside a closed surface times the area of the surface is proportional to the net charge

inside the surface.

2. The figure below shows a few equipotential surfaces surrounding two point charges. The voltages of theequipotentials are indicated on the diagram. Based on the figure, what is the sign of (i) the charge on theleft, and (ii) the charge on the right?

A) (i) Negative, (ii) Negative.B) (i) Positive, (ii) Positive.C) (i) Negative, (ii) Positive.D) (i) Positive, (ii) Negative.E) Cannot say definitely without more information.

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3. How many electrons should be removed from an initially uncharged spherical conductor of radius 0.30 mto produce a potential of 7.50 kV at the surface? (assume the potential at infinity is 0 Volts)

A) 2.5× 10−7

B) 1.2× 1016

C) 2.5× 1014

D) 1.6× 1033

E) 1.6× 1012

4. Suppose you have a parallel plate capacitor with plate-separation d. If you move the plates so thatd→ d/2 (that is, the plate-separation decreases by a factor of 2), what happens to the energy stored in thecapacitor? Assume that the charge on the capacitor remains unchanged when you move the plates.

A) It decreases by a factor of 4.B) It decreases by a factor of 2.C) It remains the same.D) It increases by a factor of 2.E) It increases by a factor of 4.

5. What is the direction of the net force on the particle lying on the positive x-axis? The particles are atpositions (x, y) = (±2d, 0) and (0, 3d).

A) Up and right.B) Up and left.C) Down and right.D) Down and left.E) Zero.

6. Suppose we have two metal spheres far away from each other: the first has radius R1 and net charge Q1,and the second has radius R2 < R1 and net charge Q2 > Q1. If we take a metal wire and connect the twospheres, what will be the same for the two spheres after the two come to equilibrium? (Careful! If more thanone of the following is true, then the answer is D or E.)

A) The charges of the spheres.B) The electric fields at the surface of the spheres.C) The electric potentials at the surface of the spheres.D) Two of the things in answer choices A-C.E) All three of the things in answer choices A-C.

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7. A proton is released from rest in a uniform electric field of magnitude 9.0 × 103V/m directed along thepositive x axis (see the figure below). The proton undergoes a displacement of magnitude d = 0.30m in the

direction of ~E. What is the change in potential energy of the charge-field system for this displacement? Themagnitude of the charge of the proton is 1.602× 10−19 Coulombs.

A) −1.7× 10−22 JoulesB) 1.7× 10−22 JoulesC) −1.4× 10−15 JoulesD) −4.3× 10−16 JoulesE) 4.3× 10−16 Joules

8. What is the magnitude of a point charge that would create an electric field 1 N/C at a point 40cm away?

A) 2× 10−5 CB) 4× 102µCC) (3× 108)eD) (1× 108)eE) 4× 10−5µC

9. The following graph shows the electric field as a function of radius for a spherical charge distribution,where ES = 5× 107 N/C. What is: (i) The charge distribution, and (ii) the total charge?

A) (i) Spherical shell of radius 2cm, (ii) 2 mC.B) (i) Spherical shell of radius 2cm, (ii) 0.7 µC.C) (i) Uniformly-charged sphere of radius 2cm, (ii) 0.7 mC.D) (i) Uniformly-charged sphere of radius 2cm, (ii) 2 µC.E) (i) Spherical shell of radius 2cm, (ii) 2 µC.

10. How much work is required to turn an electric dipole 180◦ in a uniform electric field of magnitudeE = 146.0 N/C if the dipole moment has a magnitude of p = 3 × 10−25 C ·m and the initial angle betweenthe dipole moment and the electric field is 30◦?

A) 4× 10−23 JoulesB) 2× 10−22 JoulesC) 4 eVD) 0.5 meVE) 8× 10−24 Joules

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11. What is the x-component of the Electric Field at the point (3x− 4y + 3z) m if the electric potential inthe region is given by V (x, y, z) = 5x2yz3, where V is in Volts and (x, y, z) are in meters?

A) 120 N/CB) 3.24 kN/CC) −120 VD) −3.24 kV/mE) None of the above.

12. A charge −q < 0 is distributed uniformly on a one-dimensional rod of length L which lies along thex-axis. The electric field at point P has magnitude EP . Consider the following three statements:• Statement 1: The electric field at P points to the left.• Statement 2: EP < k|q|/(a+ L/2)2.• Statement 3: The linear charge density of the rod is λ = q/L.

Which of the above statements is/are TRUE?

A) Statement 1 only.B) Statement 2 only.C) Statement 3 only.D) Statements 1 and 3.E) Statements 2 and 3.

13. A parallel-plate capacitor is connected to a battery of electric potential difference V . If the plateseparation is increased, do the following quantities increase, decrease, or remain the same? (i) the capacitor’scapacitance, (ii) the charge on the capacitor, (iii) the energy density of the electric field inside the capacitor?

A) (i) increases, (ii) decreases, (iii) remains the same.B) (i) decreases, (ii) decreases, (iii) remains the same.C) (i) increases, (ii) remains the same, (iii) decreases.D) (i) decreases, (ii) increases, (iii) decreases.E) (i) decreases, (ii) decreases, (iii) decreases.

14. The figure shows two disks and a flat ring, each with the same uniform charge Q. Point P for each figureis the same distance away from the center of the disk/ring. Which configuration has the smallest magnitudeof the electric field at point P?

A) (a) only.B) (b) only.C) (c) only.D) (a) = (b).E) (a) = (b) = (c).

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15. You are to connect capacitors with capacitances C1 and C2 (with C2 > C1) to a battery four ways: (i)just with C1, (ii) just with C2, (iii) with C1 and C2 in parallel, and (iv) with C1 and C2 in series. Rank thosearrangements according to the amount of charge stored, greatest first.

A) (iii), (i), (ii), (iv).B) (iii), (ii), (i), (iv).C) (i), (iv), (iii), (ii).D) (i), (iii), (iv), (ii).E) (i), (ii), (iii), (iv).

16. A charged particle is held at the center of two concentric conducting spherical shells A and B, eachwith an inner and outer surface (a cross-section is shown). Also shown is a plot of the net flux ΦE througha Gaussian spherical shell centered on the particle, as a function of the radius r of the shell. What is thecharge on the inner surface of conductor B? The value of ΦS in the plot is 5.0× 105 N ·m2/C.

A) 4.4µC.B) −3.5µC.C) 8.0µC.D) −4.4µC.E) −1.8µC.

End of Exam

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