Physics 202 MWF 12:40 Spring 1993 (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 very small object with negative charge q = -5.0 × 10^-4 C and mass m = 5.0 × 10^-8 kg is traveling with constant speed v = 4.0 × 10³ m/s. The object enters a region of uniform magnetic field and travels in the semicircular path of radius R = 15.0 cm shown in the sketch. What are the magnitude and direction of the magnetic field in the region?

Ans. B = __2.67 T__

direction __out of page__


(14 pts) 2. A potential difference of 500 V is established between two very large parallel metal plates that are 2.0 cm apart.

a) An electron (mass 9.11 × 10^-31 kg and charge -1.6 × 10^-19 C) is released from rest just above the negative plate A. What is the speed of the electron just before it reaches the positive plate B? Neglect the effects of gravity.

Ans. __1.33 × 10⁷ m/s__

b) What are the magnitude and direction of the electric field produced by the two plates at a point 0.5 cm below the positive plate and therefore 1.5 cm above the negative plate? (Give the direction as either from A to B or from B to A.)

Ans. E = __2.5 × 10⁴ V/m__

direction __B to A__

c) Use Gauss's law to calculate the surface charge density (charge per unit area ) on the bottom surface of plate B.

Ans. __2.21 × 10^-7 C/m²__


(12 pts) 3. A negative point charge q₁ = -6.0 × 10^-9 C is placed at the origin and a positive point charge q₂ = +8.0 × 10^-9 C is placed on the y-axis at y = +3.0 m

a) On the sketch given below show clearly the directions of the electric fields E₁ and E₂ at point P due to each of the two point charges. Point P is on the x-axis at x = 4.0 m.

b) Calculate the x- and y-components of the resultant electric field at point P due to these two point charges.

Ans. E_x = __-1.08 N/C__

E_y = __-1.73 N/C__

c) Calculate the resultant electric potential V at point P due to these two point charges.

Ans. __+0.9 V__


(12 pts) 4.
a) In the circuit shown below, after the currents have reached their final values what is the charge on each of the two capacitors?

Ans. Q₁ = __72 × 10^-6 C__

Q₂ = __180 × 10^-6 C__

b) In the circuit shown below, after the currents have reached their final values what is the charge on each of the two capacitors?

Ans. Q₁ = __112 × 10^-6 C__

Q₂ = __112 × 10^-6 C__


(10 pts) 5. Two long, straight, parallel wires are 4.0 cm apart and carry currents I₁ and I₂ in opposite directions as shown in the sketch. Calculate the magnitude and direction of the resultant magnetic field at a point P that is 1.0 cm from the top wire and 5.0 cm from the bottom wire?

Ans. B = __3.6 × 10^-5 T__

direction __out of page__


(10 pts) 6. In the sketch below the rod GH 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 is pulled to the left at constant speed v = 40.0 m/s by an external force F_ext. Calculate the current induced in the rod. Is the direction of the induced current from G to H through the rod or from H to G?

Ans. I = __8 A__

direction __H to G__


(12 pts) 7. 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 = +30 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. __100 cm, to left of lens__

b) Is the final image real or virtual?

Ans. __virtual__


(7 pts) 8. The current through an inductor is from left to right as shown in the sketch and is decreasing at a uniform rate of -0.05 A/s. The inductance of the inductor is L = 0.60 H.

a) What is the potential difference V_ab across the inductor?

Ans. __0.03 V__

b) Which point, a or b, is at higher potential? Ans. __point b__


(6 pts) 9. What is the de Broglie wavelength of an electron that has been accelerated through a potential difference of 120 V, so the electron has an energy of 120 eV? (An electron has mass 9.11 × 10^-31 kg and charge -1.6 × 10^-19 C.)

Ans. __0.112 nm__


(8 pts) 10. The nucleus ²¹⁸₈₄Po decays by -particle emission with a half-life of 3.05 min.

a) What are the mass number A (number of nucleons) and atomic number Z of the nucleus produced by this decay?

Ans. A = __214__

Z = __82__

b) If a sample contains 5.0 × 10²⁰ radioactive ²¹⁸₈₄Po nuclei, how many -particles are emitted each second?

Ans. ____1.89 × 10¹⁸ s^-1__

c) If a sample initially contains 5.0 × 10²⁰ radioactive ²¹⁸₈₄Po nuclei, how many ²¹⁸₈₄Po nuclei are left after 6.10 min?

Ans. __1.25 × 10²⁰__