Physics 202 MWF 10:20 Spring 1997 (Ford)
Final Exam

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


(8 pts) 1. The potential difference V_ab across the terminals of a battery is 9.5 V when there is a current of 3.00 A in the battery from the negative to the positive terminal. When the current is 2.00 A in the reverse direction the potential difference V_ab becomes 11.5 V. What are the emf and internal resistance r of the battery?

Ans. __10.7 V__

Ans. r = __0.4 ________________


(12 pts) 2. In the circuit shown in the sketch, = 160 V, C₁ = 5.0 × 10^-6 F, C₂ = 3.0 × 10^-6 F, R₁ = 8.0 , R₂ =20.0 , R₃ =15.0 , and L = 2.0 H. The capacitors initially have no charge.

Just after the switch S is closed, what is

a) the current in R₁   Ans. __20 A__

b) the current in R₂   Ans. __8 A__

c) the current in R₃   Ans. __0__

After the switch has been closed a long time and all currents have reached their final values, what is

a) the charge on C₁   Ans. __8.0 × 10^-4 C__

b) the charge on C₂   Ans. __4.8 × 10^-4 C__

c) the current in R₁   Ans. __0__

d) the current in R₂   Ans. __8 A__

e) the current in R₃   Ans. __10.7 A__


(12 pts) 3. A point charge q₁ = +2.0 × 10^-6 C is placed at the origin and a point charge q₂ = -6.0 × 10^-6 C is placed on the x-axis at x = 1.0 m. Point A is on the x-axis at x = 0.2 m and point B is on the x-axis at x = 0.7 m.

a) What the resultant electric field (magnitude and direction) at point A produced by the two charges q₁ and q₂?

Ans. magnitude __5.34 × 10⁵ N/C__________________

direction __to the right__

b) A third point charge, q₃ = +3.0 × 10^-6 C, is released from rest at point A. What is its kinetic energy when it reaches point B?

Ans. __0.530 J__


(12 pts) 4. A parallel plate capacitor has plates separated by 3.0 × 10^-3 m and has air between the plates. The capacitor is connected to a battery with emf = 40 V and the charge on each plate of the capacitor is found to have magnitude Q = 8.0 × 10^-9 C. While the capacitor is still connected to the battery, a dielectric with dielectric constant K = 8 is inserted between the plates, completely filling the volume between the plates.

a) What is the capacitance C of the capacitor after the dielectric has been inserted?

Ans. __1.6 × 10^-9 F________________

b) What is the area of each plate of the capacitor?

Ans. __0.0678 m²__

c) Before the dielectric is inserted, what is the magnitude of the electric field at a point between the plates, 1.0 × 10^-3 m from the postively charged plate?

Ans. __1.33 × 10⁴ V/m__

d) After the dielectric is inserted, what is the magnitude of the electric field at a point between the plates, 1.0 × 10^-3 m from the postively charged plate?

Ans. __1.33 × 10⁴ V/m__


(10 pts) 5. A very small object with charge q and mass m = 3.0 × 10^-8 kg is traveling with constant speed v = 4.0 × 10³ m/s. The object enters a region of uniform magnetic field with B = 2.0 T and that is directed into the page. In the magnetic field region the object travels in a semicircular path of radius R = 8.00 cm as shown in the sketch.

a) What is the magnitude of the charge q of the object?

Ans. ____7.5 × 10^-4 C__

b) Is the charge q positive or negative?

Ans. __positive__


(12 pts) 6. 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__


(11 pts) 7. In the sketch below the rod AB makes contact with metal rails that are 0.50 m apart. The resistance of the rails plus rod 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 0.060 kg. An external force of 2.5 N is required to pull the rod to the right with constant speed v.

a) What is the speed v of the rod?

Ans. __12.5 m/s__

b) Does the induced current travel through the rod in the direction from A to B or from B to A? (Show the direction of the induced current in the sketch.)

Ans. __A to B__


(10 pts) 8. A glass sphere surrounded by air has radius R = 8.0 cm and refractive index n = 1.7. Parallel rays from a distant object are incident on the sphere.

a) How far if the final image from the center of the sphere?

Ans. __9.71 cm to right__

b) Is the final image real or virtual?

Ans. __real__


(7 pts) 9. Tritium, ³₁H, is an isotope of hydrogen that undergoes beta-minus decay with a half-life of 12.3 years.

a) How many neutrons and how many protons are in the nucleus that is produced by the beta-minus decay of tritium?

Ans. neutrons __1__

protons __2__

b) A sample initially contains 8.0 × 10¹⁶ tritium nuclei. After how many years are there 2.0 × 10¹⁶ tritium nuclei left?

Ans. __24.6 years__

c) If the mass of a neutral tritium atom is 3.01605 u, how much energy is released in the beta-minus decay of tritium? Express your answer in MeV. The atomic mass of ³₂He is 3.016030 u.

Ans. __0.019 MeV__


(6 pts) 10. For a given metal surface, the longest wavelength of light that will cause photoelectrons to be emitted is 500 nm.

a) What is the work function for this surface? Express your answer in eV.

Ans. __2.48 eV__

b) What wavelength of light is required to produce photoelectrons from this surface that have a maximum kinetic energy of 3.0 eV?

Ans. __226 nm__