Physics 202 MWF 10:20 Spring 2001 (Ford)
Final Exam

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


(9 pts) 1. A point charge of q = +5.0 × 10^-6 C is held fixed in place. From a horizontal distance of 0.060 m a small sphere of mass 4.0 × 10^-3 kg and charge +2.0 × 10^-6 C is fired with an initial speed of 40 m/s toward the fixed charge. Gravity can be neglected. How far is the small sphere from the fixed charge when its speed is 15 m/s?


Ans.___0.0212 m___


(10 pts) 2. Point charges q₁ = -4.0 × 10^-9 C and q₂ = +6.0 × 10^-9 C are held fixed on the x-axis as shown in the sketch. Point P is at the origin.



a) What are the magnitude and direction of the resultant electric field at point P produced by these two charges?

Ans. E = ____300 N/C___

direction __+x__________

b) A third point charge q₃ = -8.0 × 10^-9 C is placed at point P. What are the magnitude and direction of the resultant force on q₃ exerted by the electric field of the other two charges?

Ans. F = ___2.4 × 10^-6 N_____________

direction ___-x_________


(9 pts) 3. Three capacitors are connected to a battery as shown in the sketch. Sufficient time has passed for all the capacitors to be fully charged. Capacitor C₁ has charge q₁ = 9.0 × 10^-6 C. What is



a) the charge q₂ on C₂?

Ans. ____9.0 × 10^-6 C_______________

b) the charge q₃ on C₃?

Ans. ___2.25 × 10^-5 C________________

c) the voltage V of the battery?

Ans. ___4.5 V___


(10 pts) 4. An electron (charge q = -e = - 1.6 × 10^-19 C) is moving in the vicinity of a long, straight wire that carries a current I = 4.0 A in the direction shown in the sketch. At a particular instant the electron is 0.080 m above the wire and it is traveling at a speed of v = 6.0 × 10³ m/s in a direction perpendiuclar to the wire and toward it.



a) What are the magnitude and direction of the magnetic field produced by the current in the wire at the location of the electron? (Specify the direction as to the left, to the right, toward the top of the page, toward the bottom of the page, into the page, out of the page.)

Ans. B = ___1.0 × 10^-5 T____________

direction___out of page____

b) What are the magnitude and direction of the force that the magnetic field of the current exerts on the electron? (Specify the direction as to the left, to the right, toward the top of the page, toward the bottom of the page, into the page, out of the page.)

Ans. F = ___9.6 × 10^-21 N____________

direction___to the right___


(10 pts) 5. A rectangular loop of wire of width 0.050 m is being pulled toward the bottom of the page, as shown in the sketch, with a constant speed of v = 4.0 m/s. The loop is leaving a region in which there is a uniform magnetic field of 2.0 T directed out of the plane of the paper. The loop has resistance 0.30 .



a) What are the magnitude and direction (clockwise or counterclockwise) of the current induced in the loop?

Ans. I = ___1.33 A___

direction ___counterclockwise_____

b) What are the magnitude and direction of the force F_B that the magnetic field B exerts on the loop? (Show the direction of this force on the sketch.)

Ans. F_B = ___0.133 N_____

direction __toward top of page_____



(9 pts) 6. Consider the series RCL circuit shown in the sketch. R = 300 , L = 0.40 H and C = 6.0 × 10^-8 F. When the ac generator operates at the resonant frequency, the current amplitude in the circuit is 0.20 A.



a) What is the voltage amplitude of the generator?

Ans. _____60 V____

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

Ans. ___516 V___

c) What is the average power supplied by the generator?

Ans. ___6 W____


(10 pts) 7. An object 2.0 mm tall is placed 20 cm to the left of a converging lens which is in turn 4 cm to the left of a diverging lens. The converging lens has f₁ = +10 cm and the diverging lens has f₂ = -10 cm.



a) How far is the final image from the object?

Ans. ___2.6 cm to left___

b) Is the final image real or virtual?

Ans. ___virtual___

c) Is the final image upright or inverted?

Ans. ____upright_____

d) What is the height of the final image?

Ans. ____3.33 mm___


(10 pts) 8. Coherent light is passed through a single slit whose width is 0.30 mm. The diffraction pattern is observed on a screen 750 mm from the slit and the width of the central maximum is 6.0 mm. If electrons are used instead of light, what must be the velocity v of the electrons if they are to produce a diffraction pattern of the same width, 6.0 mm?


Ans. ____606 m/s____



(9 pts) 9. Coherent light with wavelength = 300 nm in air is incident on a soap film (n = 1.33). There is air on both sides of the film. What is the smallest thickness of the soap film (not counting zero thickness) for which there will be constructive inteference between the light reflected at the top and bottom surfaces of the film?



Ans.____56.4 nm___



(6 pts) 10. The atomic mass (electrons included of ¹¹₅B is 11.009305 u. Use this information and the masses given on the formula sheet to calculate the total binding energy of ¹¹₅B.

Ans. ___76.2 MeV____



(8 pts) 11.
a) A one-gram sample of carbon ¹¹₆C has an activity of 3.1 × 10¹⁹ decays/s. Use this to calculate the half-life of this isotope of carbon.

Ans. ___1224 s____

b) The ¹¹₆C isotope undergoes ⁺ (positron) decay. How many neutrons and how many protons are in the daughter nucleus produced by this decay?

Ans. neutrons ___6___

protons ____5___