Suppose an electric field in a region of space is given by (1) where t is a constant with units of time and bis some given constant. (a) what are the units of the constant b.? sketch the e-field in the x-y plane (by hand), and then check yourself with mathematica (hint: vector is a built in command. use mma to learn the syntax, and include your mma plot with your homework.) (2) (b) calculate the closed line integral e. al where l is a circle of radius r, parallel to the x-y plane, centered at (0,0,2). integrate counterclockwise as viewed from "above". (i. e. viewed from +z) (c) calculate the closed line integral equation (2) again, this time where l is a rectangle (sides of length a and b, centered around the origin) oriented parallel to the x-y plane. (again, integrate counterclockwise as viewed from "above") clearly describe in words how the value of equation (2), here and in part (b), depends on b./t and the geometry of l. (d) calculate v x e and describe the resulting vector field in words. show that the closed line integral values in (b) and (c) are equal to the corresponding surface integrals of v x e. relate this to stokes' theorem! (e) determine the scalar potential that gives equation (1) (or explain why no such potential exists.) finally - describe how you could use such a static electric field to make a lot of money and save the world. does the electric field in this problem violate any of maxwell's equation for a static situation?

19. explain why a magnet from your refrigerator could not be used to lift something as heavy as a car. (chapter 7 – pages 202-203) 20. can a magnet ever have a single pole? explain your answer. (chapter 7 – page 208) 21. what happens to the wavelength of a wave if the frequency is increased? (chapter 9 – pages 280-281) 22. an ocean wave has a wavelength of 10 m and a frequency of 4.0 hz. what is the velocity of the wave? show the appropriate equation from your book and show your work with units. (chapter 9 – page 282) 23. as you sit outside, the sound of a siren becomes lower in pitch. is the emergency vehicle moving away from or towards you? explain how you know. (chapter 10 – page 315-316) 24. why are two astronauts in space unable to hear one another? (chapter 10 – page 307) 25. explain in at least 3 sentences how electromagnetic waves form. (chapter 11 – page 338-339) 26. using the chart on page 345 in your textbook, what are the three types of electromagnetic wave with wavelengths shorter than those of visible light. give an example of each. (chapter 11 – pages 345-351) 27. explain why a leaf usually appears to be green, but a rose typically appears red. (chapter 12 – page 373) 28. what is the difference in light that is refracted compared to light that is reflected? think in terms of speed of light as well as what happens to light waves when they interact with a medium. (chapter 12 – pages 369-370) 29. how are concave and convex lenses different? (chapter 13 – page 408-410) 30. what type of mirror is used in rearview mirrors in cars? why is it important that these mirrors have the warning, “objects in mirror are closer than they appear.”? (chapter 13 – page 405)

In a set amount of time, a battery supplies 25j of energy to an electric circuit that includes two different loads. one of the loads produces 10 j of heat energy during this time interval. how much heat energy is produced by the second load in this time? explain your answer

Which of the following is the best name for mgcl2