3. Total charge Q is uniformly distributed throughout the volume R≤ Ro, where Ro is a constant. Using Gauss's law, determine: (a) the volume charge density, pv. (b) Ē for R < Ro. (c) Ē for R > Ro. (d) the potential, V, at R = 2R, m.

8: Two (infinite) wires carrying a current I are hung from strings of length L = 0.06 m.Each wire has a mass per unit length of 0.04 kg/m. If 0 = 16°, find I. Are the currents in the same direction or in opposite directions? Explain.

Write the oxidation and reduction half-reactions for this process.

Find Is, In and I2 in the circuit below, given the currents shown.

6. (Optional) The circuit shown is linear and time-invariant. a. Write the differential equation with vc as the dependent variable, and indicate theproper initial conditions as functions of vc(0), and i¿(0). Hint: Write a KCL atnode 1, expressing i, in terms of vc and its derivative, and then a KVL in termsvc as an independent variable. b. Calculate the zero-input response vc(t), and i¿(t). Assume i¿ (0) = 1A, and%3D v_{c}(0)=4 V . R_{1}=4 \Omega, R_{1}=2 \Omega, L=1 H, \text { and } C=\frac{1}{2} F

LVcVs++1 8. In the linear time-invariant circuit below, Before time t = 0 the switch is open, andthe voltages across the capacitors are v, = 1V, and v2 = 4V. The switch is closed attime t = 0 and remains in this condition for a time interval of t = 2n. The switch isopened at t = 2n, and remains open thereafter. What are the values of v, and v2 fort> 27?

Hot water at an average temperature of 70°C is flowing through a 15-m section of a cast iron pipe (k- 52 W/m K) whose inner and outer diameters are 4 cm and 4.6 cm, respectively, The outer surface of the pipe is exposed to the cold air at 10°C in the basement, with a heat transfer coefficient of 15 W/m2-K. The heat transfer coefficient at the inner surface of the pipe is 120 W/m2-K. Ignoring radiation determine the rate of heat loss from the hot water in W.

3.51 For the vector field D = R3R², evaluate both sides of the divergence theorem for the region enclosed between the spherical shells defined by R =1 and R = 2.

A periscope consists of two 90-45-45º prisms (as shown in Figure) are made of lossless glass with n=1.5. The reflection off the inclined planes are 100% (total reflection per Snell's Law), i.e. |T|= 1. (a) What power(in dB) is the transmitted signal through the bottom prism relative to the input? (b) If the incoming signal has a magnetic field given by: H,(x,f) = 23.77 sin(10"r-kx)mA/m, what is the first reflected E-field? What is k?feld B

A dipole and a solid sphere of charge +Q are oriented as shown in Figure. The dipole consists of two charges q and - q, held apart by a rod of length s. The center of the dipole and the sphere are at a distance d from the location A. q = 6 nC, s =4 mm, d = 14 cm, and Q = 8 nC. \text { Find the magnitude of the electric field }\left|\overrightarrow{\mathbf{E}}_{\text {dipole }}\right| \text { due to the dipole at the location } \mathbf{A} . (10 points) Draw the direction of the electric field due to the dipole at the location A and write the electric field as a vector Edipole· \text { 5) Find the net electric field vector } \overrightarrow{\mathbf{E}}_{\text {net }} \text { at location } \mathbf{A} \text { due to dipole and the solid sphere. } \text { ) If a proton is placed at location } A, \text { what would be the net electric force vector } \vec{F}_{\text {net }} \text { on the proton? } \text { Find the electric field vector } \overrightarrow{\mathbf{E}}_{\text {Solid sphere }} \text { due to the solid sphere at the location } \mathbf{A} \text {. }