Physics 202 MWF 10:20 Spring 1994 (Ford)
Final Exam
Show all your work. Partial credit will be given if earned. Write your answers in the blanks provided.


(10 pts) 1. Point charge q₁ = +1.5 × 10^-6 C is on the x-axis at x = 1.0 m and point charge q₂ = -4.0 × 10^-6 C is on the x-axis at x = 2.0 m, as shown in the sketch.

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

Ans. magnitude __4500 N/C__

direction (to the left or to the right?) __to the left__


(12 pts) 2. In the circuit shown in the sketch C₁ = 2.0 µF, C₂ = 6.0 µF, C₃ = 3.0 µF, and C₄ = 6.0 µF. The potential difference applied across the network is 40 V. Calculate the charge on each capacitor and the potential difference across each capacitor. (1 µF = 10^-6 F)

Ans. Q₁ __6 × 10^-5 C__

Q₂ __6 × 10^-5 C__

Q₃ __8 × 10^-5 C__

Q₄ __8 × 10^-5 C__

V₁ __30 V__

V₂ __10 V__

V₃ __26.7 V__

V₄ __13.3 V__


(10 pts) 3. A positive point charge q₁ = +5.0 × 10^-6 C is held fixed at the origin. A second point charge with charge q₂ and mass 2.0 × 10^-6 kg moves in along the x-axis toward q₁. At point a, on the x-axis at x = 5.0 m, the charge q₂ has speed 600 m/s and at point b, on the x-axis at x = 2.0 m, the charge q₂ has speed 400 m/s. As q₂ moves between a and b the only force exerted on it is the Coulomb force exerted by q₁. What is q₂ (sign and magnitude)?

Ans. magnitude q₂ = ____1.48 × 10^-5 C_______________

sign (+ or -?) __+__


(8 pts) 4. The circuit shown in the sketch consists of an emf, a switch, two resistors, and a capacitor. Initially the switch is open and there is no charge on the capacitor. At t = 0 the switch is closed.

a) Just after the switch is closed, what is

i) the current i₁ through resistor R₁?

Ans. __6 A__

ii) the current i₂ through resistor R₂?

Ans. __0__

iii) the potential difference v_ab between points a and b?

Ans. __0__

b) A long time after the switch is closed, what is

i) the current i₁ through resistor R₁?

Ans. __2.4 A__

ii) the current i₂ through resistor R₂?

Ans. __2.4 A__

iii) the potential difference v_ab between points a and b?

Ans. __7.2 V__


(8 pts) 5. The circuit shown in the sketch consists of an emf, a switch, two resistors, and an inductor. Initially the switch is open and there are no currents. At t = 0 the switch is closed.

a) Just after the switch is closed, what is

i) the current i₁ through resistor R₁?

Ans. __2.4 A__

ii) the current i₂ through resistor R₂?

Ans. __2.4 A__

iii) the potential difference v_ab between points a and b?

Ans. __7.2 V__

b) A long time after the switch is closed, what is

i) the current i₁ through resistor R₁?

Ans. __6 A__

ii) the current i₂ through resistor R₂?

Ans. __0__

iii) the potential difference v_ab between points a and b?

Ans. __0__


(10 pts) 6. A particle with charge q = -3 × 10^-6 C is moving to the right with speed v = 5 × 10⁵ m/s in a region where there are perpendicular electric and magnetic fields. The magnetic field has magnitude 0.3 T and is directed into the plane of the paper.

a) What are the magnitude and direction (up, down, right, left) of the force that the magnetic field exerts on the particle?

Ans. magnitude __0.45 N__

direction __down, toward bottom of page__

b) What must be the magnitude and direction (up, down, right, left) of the electric field in the region if the particle is to move in a straight line with constant speed through the region? (Neglect gravity.)

Ans. magnitude ____1.5 × 10⁵ N/C_____________

direction __down, toward bottom of page__


(7 pts) 7. Coherent light of wavelength 500 nm passes through two narrow slits A and B and an interference pattern is produced on a screen. Point P on the screen is the location of the second minimum above the central maximum. Let l₁ be the distance from slit A to point P and l₂ be the distance from slit B to point P. What is l₂ - l₁, the difference between these two distances?

Ans. __750 nm__


(10 pts) 8. Parallel rays from a very distant object are incident from the left on the two thin lenses shown in the sketch. The converging lens has f₁ = +35 cm and the diverging lens has f₂ = -20 cm. The distance between the two lenses is 5 cm.

a) How far is the final image from the second lens?

Ans. __60 cm to left__

b) Is the final image real or virtual?

Ans. __virtual__


(9 pts) 9. In the sketch below the rod AB makes contact with metal rails that are 0.50 m apart. The resistance of the rail plus rod plus circuit is 5.0 and may be considered to be constant. There is a uniform magnetic field with magnitude B = 2.0 T and direction out of the plane of the paper. The rod has mass 0.040 kg. The rod is pulled to the left at constant speed v = 7.0 m/s by an external force F_ext.

a) Calculate the magnitude of the induced current.

Ans. __1.4 A__

b) Is the direction of the induced current in the rod from A to B or from B to A? (Show the direction of the induced current on the above sketch.)

Ans. __A to B__

c) Calculate the magnitude F_ext of the external force that is required to maintain this speed.

Ans. __1.4 N__


(9 pts) 10. Consider the fusion reaction
³₂He + ²₁H -------> ⁴₂He + ¹₁H
Compute the energy liberated in this reaction, in MeV.
(1 u = 1.661 × 10^-27 kg. The mass of a proton is 1.007276 u, the mass of a neutron is 1.008665 u, and the mass of an electron is 0.000549 u.)

Ans. __18.4 MeV__


(7 pts) 11. If two gamma-ray photons of the same energy are produced in e⁺e^- annihilation (the annihilation of an electron with a positron), find the wavelength of each photon. (The mass of an electron is 9.11 × 10^-31 kg.)

Ans. __2.42 × 10^-12 m__