Problem 2 (10 points) (Chap 4) (Learning objective: surface integration in different coordinates) Calculate the areas of the following surfaces using the differential surface area dS: (a) p = 2,0

3) In above figure, current flows through a truncated circular cone of conductivity o = 10* (S/m). Left radius of the cone is a= 1 cm, right radius of the cone is b = 2 cm, and length of the cone is L = 0.2 m. The z-axis given in the figure is the rotation axis of the cone. a) Assume that this resistance is fed by DC voltage as shown in figure. Then, the electric field intensity E inside the conductor becomes only dependent on z variable but not p and/or o variable. For this DC case, what is DC resistance of this cone structure? b) Assume that DC voltage source is replaced with high frequency AC voltage source. For this case, in addition to dependency on z variable, the electric field intensity E inside the conductor is also directly proportional with p as being more realistic condition/model for high frequency AC circuits. Then, what is high-frequency AC resistance of this cone structure?

Problem 5: Wire with a hole Consider an infinitely long cylindrical conductor wire of radius b, the cross section of which is as shown in the figure. The wire contains an infinitely long cylindrical hole of radius a parallel to the axis of the conductor. The axes of the two cylinders are apart by a distance d such that d+a < b. The wire carries a total current I. a Use Ampere's law and the superposition principle to calculate B field in the hole. b Find the vector magnetic potential A inside the hole. c Use A to find the B field in the hole and show if it is the same result as in problem a.

1. A thin rod of length W has uniform charge per length A. Find the electric potential (voltage) at the position P as shown. Assume V = 0 at r = o for problems on this worksheet. Use the integration variable u as defined in the diagram to write the voltage at point P. Include the limits of integration but you do not need to evaluate the integral. P Hint: break up the rod into small pieces of length du and use the point charge formula for the voltage due to the small piece dV = Kdq/r with dą and r written in terms of the givens à, L, z and integration variable u and du. W 3 du 0.

2) If the angle the displacement makes with the electric field is 0° it means the charge is moving along (or parallel to) the field vectors. Is work being done? How will the angle here affect the work done, explain your answer with a diagram? Last Revised 12/21/2015 Equipotential Surfaces – 3.1

4) Electric field of a rod. Consider a nonconducting rod of length L with a charge q uniformly distributed along its length. We want to know the magnitude of the electric field a distance x away from one end as shown below. X L, with q evenly distributed Explain why EACH of the four answers below is WRONG. Consider symmetry, dimensions, unit analysis, behavior in limiting cases, and/or behavior at particular positions. You SHOULD NOT actually solve the problem and your answer shouldn't be because the correct answer is this. This is good practice in considering the nature of your answer... а) Е: b) E = 4πε, L(x + L) 4TE,x(x – L) c) E = d) E = 4л, (х? + L/4) 4лєрх(2х + L) 5) Electric field of a rod again--this time with calculus and a different geometry •Part a: A thin nonconducting rod of length L has charge q uniformly distributed along it as shown in Fig. 22-55 (associated with problem 32). SHOW that the magnitude of the electric field at point P (on the perpendicular bisector of the…

Q1. a) () Describe in words how you might apply Gauss's law to a closed surface to determine the free charge enclosed. Describe the two most useful Gaussian surfaces. Where are they used and what differences must be accounted for when applying them? (ii)

a. Convert from Cartesian to cylindrical and spherical coordinates: 1. P(-2.0, 3.0, 2.0) b. Convert the from cylindrical to Cartesian coordinates: 1. P(2.83, 45.0°, 2.00)

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