True or false for question 1: if false exlplain why A)The directed derivative of the voltage gives a vector that points in the direction of the closest local maximum of the voltage. Due to the minus sign in the relationship between E~ and V , it can be concluded that electric fields point from high voltages to low voltages, otherwise known as “downhill” B) ) The equation E = −∆V/∆l is always true, for every situation.

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for y d €0 result, use this potential next. aV i+ i+ k) for y < 0, 0 < y < d 6. (a) Now compute -VV and d < y. - (b) Should your result agree with the electric field E that you calculated in problem 2? Does it agree? 7. What is the value of the integral f E· dr over a closed path? You need to be special clear and compelling here to arn the points. 8. (a) Describe the equipotential surfaces with V = –5,000 Volts. Where are they located? (b) Is there an equipotential volume? If the answer is "yes," describe it. (c) Describe all the equipotential surfaces V = V, for Vo < 0 fixed but arbitrary. Where are they located as a function of Vo?

Consider two long, parallel, and oppositely charged wires with linear charge density +λ and -λ of radius r with their centers separated by a distance D (? ≫ ?). Show that the capacitance per unit length of this pair of wires is given by the following,     and show the work required to set up an integral for E, ∆? and then finding C.