Physics 202 MWF 10:20 Spring 2002 (Ford)

Exam I Chapts. 18 and 19 in Cutnell and Johnson 5th ed.

Multiple choice questions. Circle the correct answer. No work need be shown and no partial credit will be given.

A solid conducting sphere has radius R = 0.2 m and carries a net positive charge. The electric potential at the surface of the sphere is +200 V.

(3 pts) 1. The electric field at the center of the sphere is
(a) infinite

(b) zero <------------
(c) 1000 V/m
(d) 5000 V/m


(3 pts) 2. The electric potential at the center of the sphere is

(a) infinite
(b) zero
(c) 200 V <----------
(d) 1000 V


A uniform electric field is directed toward the top of the page as shown. Point B is directly below point A and point C is directly to the right of point A.


(3 pts) 3. The following is true about the electric potential at points A and B:

(a) V_A > V_B
(b) V_A = V_B
(c) V_A < V_B <----------


(3 pts) 4. The following is true about the electric potential at points A and C:

(a) V_A > V_C
(b) V_A = V_C <---------
(c) V_A < V_C


Show all your work. Partial credit will be given if earned. Write your answers in the blanks provided.


(20 pts) 5. A point charge q₁ = -6.0 × 10^-9 C is located on the +x-axis at x = +0.05 m. A point charge q₂ is located on the -x-axis at x = -0.02 m. The resultant electric field produced by these two point charges is zero at the origin (x =0).


a) What is the magnitude of q₂ and is it positive or negative?

Ans. magnitude ___9.6 × 10^-10 C___

positive or negative? __negative__

b) What is the resultant electric potential at the origin produced by charges q₁ and q₂? Take V = 0 at large distances from both charges.

Ans. ___- 1512 V___________


(18 pts) 6. A small spherical insulator of mass 0.05 kg and charge q₁ = -6.0 × 10^-9 C is suspended by a thread. A charge q₂ is held 0.20 m to the right of q₁ and the thread makes an angle of 53° with respect to the vertical.


a) What is the tension T in the thread?

Ans. ____0.817 N____

b) What is the magnitude of q₂ and is it positive or negative?

Ans. magnitude ____4.83 × 10^-4 C_____

positive or negative? ___positive___


(16 pts) 7. A small particle has charge -6.0 × 10^-3 C. It moves from point A, where the electric potential is V_A = +200 V, to point B. The electric force is the only force acting on the particle. The particle has kinetic energy 6.0 J at point A and 4.0 J at point B. What is the electric potential V_B at point B?

Ans. ___- 133 V____


(16 pts) 8. A parallel plate capacitor has a capacitance C when the volume between the plates is filled with a dielectric that has dielectric constant =4.0. The capacitor is fully charged by connecting it to a 12 V battery, and this puts a charge of 6.0 × 10^-5 C on each plate. The capacitor is disconnected from the battery without any of the charge leaving the plates. The dielectric is then removed, so that there is now air between the plates. The charge on the plates is still 6.0 × 10^-5 C. After the dielectric is removed,

a) what is the capacitance of the capacitor?

Ans. ___1.25 × 10^-6 F____

b) what is the potential difference between the plates of the capacitor?

Ans. ___48 V___


(18 pts) 9. Two spherical shells have a common center. The inner shell has radius R₁ = 0.05 m and charge q₁ = +3.0 × 10^-6 C spread uniformly over its surface. The outer shell has radius R₂ = 0.15 m and charge q₂ = -5.0 × 10^-6 C spread uniformly over its surface.


a) What is the electric flux through a gaussian sphere that is concentric with these two shells and has radius r = 0.20 m? (This gaussian sphere lies outside both shells.)

Ans. ___- 2.26 × 10⁵ N·m²/C____

b) What is the magnitude of the electric field at a distance of r = 0.10 m from the common center of the two shells? (This distance is in the air space between the two shells.)

Ans. ___2.7 × 10⁶ N/C___

c) What is the magnitude of the electric potential at a distance of r = 0.10 m from the common center of the two shells? (This distance is in the air space between the two shells. Take V = 0 at large distances from the shells.)

Ans. ___- 3 × 10⁴ V___