An electric potential function is given by V(x, y) = 3xy^2 - 2x^2 y - 2 where MKS units are used. Show all work neatly. Don't forget to include units in your answers. Use the back if more room is needed, but note accordingly. What is the electric field vector, E(x, y), in rectangular coordinates? What is the magnitude and direction of the electric field at the point (x,y) = (2,3)? What is the divergence of the electric field at the point (x,y) = (2,3)? What is the curl of the electric field at the point (x,y) = (2,3)?

Please fill out the template with the work for this problem. Note that you need to have a picture, list of knowns and unknowns, the general equation/s you will use, the math steps to solve for the unknown, only plug in the numbers after you have solved for the unknown, and the answer with units included.

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?

Please show steps