Physics 202 MWF 10:20 Spring 2000 (Ford)
Final Exam

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


Note:
₀ = 8.85 × 10^-12 C²/N·m²
µ₀ = 4 × 10^-7 T·m/A
c = 3.00 × 10⁸ m/s
h = 6.63 × 10^-34 J·s
e = 1.60 × 10^-19 C
1 eV = 1.60 × 10^-19 J


(10 pts) 1. A point charge q₁ = +5.0 × 10^-6 C is held fixed at the origin. A second point charge with mass m = 0.040 kg and charge q₂ = +7.0 × 10^-6 C is released from rest at a distance of 0.30 m from the first charge. What is the speed of q₂ when it reaches point P, a distance of 0.50 m from q₁?

Ans. ___4.58 m/s____


(11 pts) 2.

a) Calculate the magnitude and direction of the resultant electric field at point P produced by charges q₁ = -6.0 × 10^-6 C and q₂ = +6.0 × 10^-6 C placed as shown in the sketch. (q₁ is on the y-axis at y = 0.30 m; q₂ is on the y-axis at y = -0.30 m. Point P is on the x-axis at x = 0.40 m.)

Ans. magnitude ____2.60 × 10⁵ N/C_____

direction ____+y-direction_____

b) A third charge q₃ = -3.0 × 10^-6 C is placed at point P. What are the magnitude and the direction of the resultant force exerted on q₃ by the other two charges?

Ans. magnitude ___0.78 N_____

direction ____-y-direction____


(11 pts) 3. Consider the circuit shown in the sketch.

C₁ = 3.0 µF
C₂ = 3.0 µF
C₃ = 1.0 µF
C₄ = 2.0 µF

a) Calculate the charge on each capacitor.

Ans. q₁ ____15 µC_____

q₂ ____15 µC_____

q₃ ____10 µC___

q₄ ____20 µC___

b) Find the potential difference V_a - V_b. Which point, a or b, is at higher potential?

Ans. V_a - V_b ____5 V____

point at higher potential is ____a____

b) Find the potential difference V_b - V_c. Which point, b or c, is at higher potential?

Ans. V_b - V_c ____10 V____

point at higher potential is ____b_____


(10 pts) 4. Consider the circuit shown in the sketch below.

a) Calculate the emf's ₁ and ₂. Note that two currents are given.

Ans. ₁ = _____8 V____

₂ = ____17 V____

b) Find the potential difference V_a - V_b. Which point, a or b, is at higher potential?

Ans. V_a - V_b ____- 7 V___

point at higher potential is ____b____


(9 pts) 5. Consider the RLC ac circuit sketched below. The circuit elements have values R = 400 , C = 4.0 × 10^-6 F, and L = 3.0 H. The source has voltage amplitude 180 V and is operated at the resonant frequency of the circuit.

a) What is the impedance Z of the circuit?

Ans. ____400 _____

b) What is the amplitude of the voltage across the resistor?

Ans. ____180 V____

c) What is the amplitude of the voltage across the inductor?

Ans. ____390 V____

d) What is the average power delivered by the source to the circuit?

Ans. ____40.5 W____


(9 pts) 6.

a) The current I in the long straight wire is increasing. Show on the sketch the direction of the induced current through R.



b) The emf in circuit A is decreasing. Show on the sketch the direction of the induced current through R.



c) The bar in the sketch is being pulled to the left on conducting rails. The magnetic field is directed into the page. Show on the sketch the direction of the induced current in the resistor R.




(8 pts) 7. Electrons with energy 0.050 eV are incident on a slit that is 0.080 mm wide. The electrons strike a screen that is 2.0 m from the slit and an interference pattern is observed. What is the width of the central maximum in the interference pattern, that is, the distance on the screen between the minima that lie on either side of the principal maximum?

Ans. ____0.274 mm____


(9 pts) 8. A thin sheet of plastic with refractive index 1.2 is on top of a flat piece of glass that has index of refraction 1.5. Coherent light of wavelength = 600 nm in air is incident perpendicular to the surface of the plastic.

a) What is the speed of the light in the plastic sheet?

Ans. ___2.5 × 10⁸ m/s_____

b) What is the wavelength of the light in the plastic sheet?

Ans. ____500 nm____

c) What is the minimum thickness of the plastic (not counting zero thickness) for which there will be constructive interference between the light reflected at the top and bottom surfaces of the plastic sheet?

Ans. ____250 nm___


(9 pts) 9. An object 3 mm tall is 40 cm to the left of a thin lens. The image is 9 mm tall and is upright.

a) Is the image real or virtual?

Ans. ____virtual___

b) How far is the image from the lens?

Ans. ____120 cm___

c) Is the lens converging (f > 0) or diverging (f < 0)?

Ans.____converging____

d) What is the focal length of the lens?

Ans. ____60 cm___


(6 pts) 10. The mass of ⁷₃Li is 7.016003 u. Use this data and that given on the formula sheet to calculate the total binding energy of ⁷₃Li.

Ans. ____39.2 MeV___


(8 pts) 11.

a) A one gram sample of radium ²²⁶₈₈Ra has an activity of 3.7 × 10¹⁰ decays/s. Use this to calculate the half-life of this isotope of radium.

Ans. ____1.6 × 10³ yr____

b) The ²²⁶₈₈Ra isotope undergoes decay. How many neutrons and how many protons are in the daughter nucleus produced by this decay?

Ans. neutrons ___136___

protons ___86___

c) The ²²⁸₈₈Ra isotope undergoes beta-minus (^-) decay. How many neutrons and how many protons are in the daughter nucleus produced by this decay?

Ans. neutrons ___139___

protons ___89___