1. Final ExamName: ID: 1.(10 points) In an X-Y coordinate system with unit in meter, charge Q1 of 7.865 μC is placed at (-1,0). Charge Q2 of -7.865 μC is placed at (1,0). A third charge Q3 of charge 1 μC is placed at (0,1), (a) What is the total force on Q3? State the magnitude and direction with respect to the coordinate system. (b) What is the electric field (both magnitude and direction) at point (0,-1)? Coulomb’s constant k = 8.99×10 9 Nm 2 /C 2. 2.(10 points) A parallel plate capacitor is constructed with two plates separated by 0.01 mm. Each plate has a surface area of 1 m 2. One plate has charge + 8.85 μC. The other plate has charge -8.85 μC, (a) what is the electric potential difference across the two plates? (b) Now you plan to double the amount of electric potential energy stored in this capacitor by connecting it to a DC power supply, what would be the voltage from this power supply? The permittivity constant ε 0 = 8.85×10 -12 C 2 /Nm 2.

2. 3.(10 points) You are given an incandescent car light bulb with a specification of 24W at 12V. (a) What is the resistance of the filament when it is operated at its specified voltage? (b) When you take an ohm meter to measure the resistance of the filament at room temperature of 20 o C, you read the resistance to be 1 ohm. If you know that when the light bulb operates at its specified voltage, the filament temperature is 1020 o C, what is the filament material’s temperature coefficient of resistively at 20 o C? 4.(5 points) An AC voltage source of V = V MAX SIN(ω · t ) is connected to a resistor array, a capacitor array and an inductor as shown in the figure. You change the angular frequency ω to achieve the minimum and maximum power dissipated through the resistors. What are the finite values of the ω that correspond to the minimum and maximum power dissipation respectively? ~ V L R C 2C 2R

3. 5.(10 points) What is the power dissipated in the system shown in the following figure? 6.(5 points) A bar magnet is thrown through a copper wire coil as shown in the following figure. The two ends of this coil are connected to an oscilloscope which measures a voltage waveform of V = V MAX SIN(ω · t ) when the bar passes through the coil. The cross section of the coil is A and the coil has N turns. (a) Write the magnetic field strength B (magnitude only) inside the coil as a function of time. At t = 0, B = 0.(b) If the oscilloscope is replaced with an ammeter and a resistor in series, indicate the current direction the ammeter reads when (1) the bar is entering the coil, (2) the bar is leaving the coil. The coil spirals up follows a right- hand direction: the thumb points upwards and the fingers follow the coil direction. 18V 6V 10Ω 12V 10Ω A C D

4. 7.(10 points) A initially charged capacitor, with charge Q 0 =1 μC, is connected to a resistor and an inductor in series as shown in the following figure. At time t = 0, the switch is closed to form a circuit. (a) if R = 0, what is the maximum current in this circuit? (b) if R = 10Ω, how much heat the resistor generates when t = 3600 second. 8.(10 points) A block made of a light crown glass with an index of refraction of 1.48 is immersed in water (n=1.33). (a) What is the critical angle of incidence if a ray is to be totally internally reflect within the glass? (b) How will that change if the water is replaced with benzene (n= 1.501)? R L=2μH C=2μF

5. 9.(10 points) Suppose you had a spherical mirror with a 2.0 m radius. If you wish to project a candle flame onto a piece of paper 1.10 m away from the mirror, where should the candle be located with respect to the mirror? Describe the image, giving the magnification as well. Draw a ray diagram. 10.(10 points) Two converging thin lenses with focal lengths of 0.30 m and 0.50 m are separated by 0.20 m. A candle is placed on the principal axis 0.50 m in front of the first lens with a focal length of 0.30 m. Locate the resulting image with respect to the second lens and its overall magnification m. 11.(10 points) A person sees objects beyond a distance of 2.0 m to be blurred, but otherwise everything seems fine. What kind of contact lenses, with what power (in diopter) should they wear?