Instructions: Read the problems carefully and answer all the questions in each problem. You are allowed to use three A4 sheets of paper with your own notes. You are NOT allowed to use any other information resources or to consult with any living person except me. Explain your answers clearly and completely. Use large, clear diagrams. You will loose points if a clear diagram is not drawn for each problem. Attach this title sheet to your solutions. Print your Last name, First name on the front. Do not fold.
1. A charge of +1.0 nanoC is uniformly distributed along the line connecting the origin and point (x=0.0 m, y=2.0 m). An additional point charge of +1.0 nanoC is placed at (x=2.0 m, y=3.0). What are the xand y-components of the vector of electric field at (x=0.0 m, y=3.0 m)?
2. A current of 1.0 A is flowing along the z-axis in the positive z direction from the origin to z=2 m. Find the magnetic field (direction and magnitude) at the following three points of interest (x,y,z):P1 (1 m, 0 m, 0 m), P2 (1 m, 0 m, 1 m), P3 (1 m, 0 m, 2 m). Which field is the strongest? Why?
3. A wire loop with an area of 2.0 m^2 and a resistance of 5.0 Ohms lies flat in the x-y plane. A spatially uniform but time-dependent magnetic field (given below) exists throughout the region. What is the induced current in the loop at t=2.0 s? Next, the loop is rotated so that it now lies in the x-z plane.
What is the induced current in the loop at t=2.0 s in this new orientation? Make a diagram clearly showing the direction of the induced current in the loop at t=2.0 s in each orientation.
4. By(t)=B0 sin(wt);Bz(t)=B0 cos(wt), where B0=1.5T and w=3.0 rad/s.A 1.0E-6 F capacitor has a charge of 10.0 microC. It is connected to a 1.0 H inductor at t=0. Find when the energy of the system is split equally between the capacitor and inductor. What is the energy of the inductor at that time moment?
5. In the circuit shown, the switch has been closed for a long time prior to t=0. At t=0, the switch is opened. What is the energy stored in the capacitor at t=1.1E-5 s ? Now, the capacitor is replaced with a 1.1 microH inductor, the circuit is reset and the switch is opened and closed as described above. What is the energy stored in the inductor at t=1.1E-5 s ?
6. A 1-microF capacitor, a 10-Ohm resistor and a 1 microH inductor are connected in series with a sinusoidal signal generator of 10V peak voltage amplitude operating at a frequency ω of 2.0E+6 rad/s.
(a) Make a phasor diagram to represent this circuit. Show the phasors of all circuit elements. Draw phasors to scale. Find the phase shift between the current and the generator voltage.
(b) How would you change this circuit to achieve resonance? Explain your reasoning.
7. A beam of light travels in air and then enters water (n=1.33) at an angle of incidence of 30 degrees. Indicate whether each statement below is true or false and explain why you think so.