Physics 202 MWF 10:20 Spring 1996 (Ford)
Exam I Chapts. 24-27 in SZY College Physics 7e
Show all your work. Partial credit will be given if earned. Write your answers in the blanks provided.


(15 pts) 1. Point charge q₁ = +8.0 × 10^-6 C is at the origin and point charge q₂ = -3.0 × 10^-6 C is on the x-axis at x = -1.0 m, as shown in the sketch. Three spherical gaussian surfaces are placed as shown in the sketch. Sphere a is centered at the origin and has radius r_a = 0.5 m. Sphere b is centered at the origin and has radius r_b = 1.5 m. Sphere c is centered at x = 2.0 m, y = 0 and has radius r_c = 0.5 m. What is the magnitude of the net electric flux through each of these spheres?

Ans. sphere a ___9.04 × 10⁵ N·m²/C___

sphere b ___5.65 × 10⁵ N·m²/C___

sphere c ___0___


(24 pts) 2. A negative point charge q₂ = -6. 0× 10^-9 C is placed at the origin and a positive point charge q₁ = +8.0 × 10^-9 C is placed on the y-axis at y = +3.0 m.

a) On the sketch given below show clearly the directions of the electric fields E₁ and E₂ at point P due to each of the two point charges. Point P is on the x-axis at x = 4.0 m.

b) Calculate the x- and y-components of the resultant electric field at point P due to these two point charges. (In your answer you must indicate whether each component is positive or negative.)


Ans. E_x = ___-1.07 N/C___

E_y = ___-1.73 N/C___

c) If a negative point charge q₃ = -3.0 × 10^-9 C is placed at point P, what are the x- and y-components of the net force that q₁ and q₂ exert on q₃? (In your answer you must indicate whether each component is positive or negative.)

Ans. F_x = ___+3.21 × 10^-9 N___

F_y = ___+5.19 × 10^-9 N___


(22 pts) 3. Point charges q₁ = -4.0 × 10^-9 C and q₂ = +5.0 × 10^-9 C are held fixed at the positions shown in the sketch. Point a is 0.10 m to the right of q₁. Point b is 0.10 m to the left of q₂ and hence 0.4 m to the right of q₁.

a) What is the total electric potential V at point a due to q₁ and q₂?

Ans. ___-247 V___

b) What is the total electric potential V at point b due to q₁ and q₂?

Ans. ___+360 V___

c) An electron (q = -1.6 × 10^-19 C and m = 9.11 × 10^-31 kg) is released from rest at point a. The electron moves along the line connecting the two charges. What is its kinetic energy as it passes through point b?

Ans. ___9.71 } 10^-17 J___


(21 pts) 4. Three capacitors are connected to a potential difference of 120 V, as shown in the sketch. The capacitors have capacitances
C₁ = 6.0 × 10^-6 F,
C₂ = 3.0 × 10^-6 F,
C₃ = 5.0 × 10^-6 F.
Calculate the magnitude of the charge Q on each capacitor and the potential V across each capacitor.


Ans. Q₁ = ___2.4 × 10^-4 C___

V₁ = ___40 V___

Q₂ = ___2.4 × 10^-4 C___

V₂ = ___80 V___

Q₃ = ___6.0 × 10^-4 C___

V₃ = ___120 V___




(18 pts) 5. A parallel-plate capacitor has capacitance C = 8.0 × 10^-6 F when there is a vacuum between its plates. The plates are separated by 0.40 mm.

a) The capacitor, with vacuum between its plates, is connected to a potential difference of 40 V. While the capacitor remains connected to the source of potential difference, a dielectric with dielectric constant K = 5 is inserted between the plates. The dielectric completely fills the volume between the plates. After the dielectric has been inserted, what is the electric field between the plates and what is the energy stored in the capacitor?

Ans. E = ___1.0 × 10⁵ V/m___

U = ___0.032 J___

b) The capacitor, with vacuum between its plates, is connected to a potential difference of 40 V. The capacitor is then disconnected from the source of potential difference and is not allowed to discharge. With the charge on the capacitor kept constant, the dielectric with K = 5 is inserted between the plates, again completely filling the volume between the plates. After the dielectric has been inserted, what is the electric field between the plates and what is the energy stored in the capacitor?

Ans. E = ___2.0 × 10⁴ V/m___

U = ___0.00128 J___