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. ___________________


(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 _________________

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 ___________________

direction ___________________


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

The capacitances of the capacitors are:
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 _____________________

q₂ _____________________

q₃ ______________________

q₄ _____________________

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

Ans. V_a - V_b _____________________

point at higher potential is _________________

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

Ans. V_b - V_c __________________

point at higher potential is __________________


(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 = ______________________

₂ = _____________________

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

Ans. V_a - V_b _________________

point at higher potential is _______________


(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. _____________________

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

Ans. _____________________

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

Ans. _____________________

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

Ans. ________________________


(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. ____________________


(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. ____________________

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

Ans. ________________________

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. ________________________


(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. ______________________

b) How far is the image from the lens?

Ans. _______________________

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

Ans.________________________

d) What is the focal length of the lens?

Ans. ______________________


(6 pts) 10. The atomic 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. ______________________


(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. _____________________

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

Ans. neutrons ___________

protons __________

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 _____________

protons __________________