#### Electrostatics

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.

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 ke- 0.1 W/m K. To reduce heat losses in the winter, the university decides to encapsulate the entire dormitory by applying an Lj- 30-mm-thick layer of extruded insulation characterized by ki- 0.029 W/m K to the exterior of the original sheathing. The extruded insulation is, in turn, covered with an Ly = 5-mm-thick architectural glass with k,-1.4 W/m K. Determine the heat flux through the retrofitted walls in W/m when the interior and exterior air temperatures are Tooi- 22°C and T.o--5°C, respectively. The inner and outer convection heat transfer coefficients are hi-5 W/m²-K and ho- 30 W/m2 K, respectively.

4. What affects the rate of deposition?

6. True or False: for a simple harmonic oscillator consisting of a mass on a spring, the period measured when the mass is hanging vertically (figure on p.2) is different than the period measured when the spring and mass are supported horizontally (figure on p.1).

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.

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?

5.7 (note: TRL = 0 because it is not given in the problem statement)

The figure shows a neutral metal, placed near two point charges. The point charges polarize the metal. Draw the approximate charge distributions on the metal due to the polarization. (9 points) At location A, draw and label the following electric fields: E1, due to charge g,, E, due to charge q2 , and Epol due to the polarization charge on the metal? What will be the net electric field at A due to all charges? \text { If } \overrightarrow{\mathrm{E}}_{1}+\overrightarrow{\mathrm{E}}_{2}=\left\langle-18 \times 10^{4}, 0,0\right\rangle \mathrm{N} / \mathrm{C}, \text { calculate } \overrightarrow{\mathrm{E}}_{\mathrm{pol}}

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.