#### Electrostatics

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.

2. Find the solution of the following linear differential equations: \text { a. } 16 y^{\prime \prime}-8 y^{\prime}+145 y=0, \quad y(0)=-2, \quad y^{\prime}(0)=1 \text { b. } y^{\prime \prime}+2 y^{\prime}+y=0, \quad y(0)=0, \quad y^{\prime}(0)=1 \text { . } \text { c. } y^{\prime \prime}+3 y^{\prime}+2 y=2+e^{-t}, \quad y(0)=0, \quad y^{\prime}(0)=-1 \text { . Hint: consider } A t e^{-t} \begin{array}{llll} \text { d. } y^{(3)}+y=\text { cost, } & y(0)=1, & y^{\prime}(0)=0, & y^{\prime \prime}(0)=0 . \end{array}

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

Insulator Conductor Semiconductor Intrinsic semiconductor Extrinsic semiconductor N-type semiconductor P-type semiconductor P-N Junction Forward biased Reverse biased Drift Current Diffusion Current Bipolar Junction Transistor (BJT) NPN PNP metal-oxide-semiconductor field-effect transistor (MOSFET) NMOS PMOS Diode-transistor (DTL) logic Resistor-transistor (RTL) logic Transistor-transistor (TTL) logic Emitter-coupled (ECL) logic Complementary MOS (CMOS) logic Bipolar CMOS (BICMOS) logic

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?

Suggest the sources of error in your experiment.

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.