4. Assume that an observer calculates electric field and potential by measuring the force on a test charge. This observer moves along the path described by the green arrow. Finally, assume the system is in vacuum. (a) Plot and justify |E| for a charged sphere-Q enclosed within an ungrounded spherical metal shell. (b) Draw all relevant field lines on the schematic (within reason). Hint: consider where the charges would be induced on the inner and outer surfaces of the shell.

1. What condition or conditions are necessary for simple harmonic motion to occur?

11: An Amperian loop surrounds a current as is shown on the left. Initially that current passes through the center of the loop. The current is then moved off center. Did the circulation of B around the loop change? In other words, did f B- ds change? Did the magnetic field on the loop change? Explain.

S. No.:Given the block-diagram representation of an airplane's pitch angle feedback control system,calculate the range of gain K value for the stable operation of the aircraft using Routh -Hurwitz method. Develop the root-locus of this system as a function of K using computer.Also determine the gain value for the damping ratio = 0.707.Compute the step response of the closed-loop system for this value of gain K. Compare it with the step response of an equivalent second-order system based on dominant poles.Develop a state variable model for this system using the previous value of gain K. Use this state variable model to find output response for a unit step.

3. Why is the measured mass different than calculated mass deposited?

A dormitory at a large university, built 50 years ago, has exterior walls constructed of L- 30-mm thick sheathing with a thermal conductivity of ks - 0.1 W/m K. Determine the heat flux through the walls in W/m2 when the interior and exterior air temperatures are Tj 22°C and To.o- 15°C, respectively.The inner and outer convection heat transfer coefficients are hi -5 W/m2-K and h. - 30 W/m2 K, respectively.

Four point charges are placed at the corners of a square with side length a = 10 cm. The charges all have the same magnitude q 10µC. Three of the charges are positive and one is negative, as shown in the figure. I. Find both magnitude and direction of the electric field at the center of the square? II. Find the electric potential at the center of the square? III. Find the total potential energy stored in the charge configuration?

Problem-2: [2x4=8pts]A crucial tool for analysis and design of semiconductor devices is energy band diagram. Understand the use of such band energy diagram is very important. Answer following questions about energy band-diagrams (i)What is a band diagram in relation to semiconductor materials? Draw a typical band-diagramfor a semiconductor material and mark the position of conduction-band, valence band and thebandgap. Why do crystal lattice (such as Si lattice) have bands of energy, while isolated Si-atoms do not have such bands?(ii) (iii)We know that electrons and holes that are responsible for conduction. But where are these located in this bands? (iv)Which direction energy of an electron increase along the y-axis of the band diagram? Energy of a hole?

5. The circuit below is made of linear and time-invariant components with: R1 =2Ω, R> = 32, C = 1/4F, and L = 1H. Vs is the input, and vc is the output.%3D a. Calculate the impulse response h(t). b. Calculate the sinusoidal steady state response (the response after the circuit hassettled for a long time) for the input vs(t) = 5cos2t, and initial conditionsvc(0-) = 1V, and i,(0-) = 2A.

1. Assume that an observer calculates electric field and potential by measuring the force on a test charge. This observer moves along the path described by the green arrow. Finally, assume the system is in vacuum. (a) Plot and justify Q, E, V for a uniformly charged cylinder of P3D, height h, radius ro where h >> ro. The path goes through the center of the prism and is perpendicular to it. Let us assume V = 0 is defined at distance 1₁. (b) Suppose the observer is far enough away that z » h. Discuss whether it is appropriate to express E, V as if the charge were a point charge.