Consider the infinite sheet of current shown in the figures. The sheet is composed of straight, parallel wires separated by distance d and each carrying current I. There are an infinite number of evenly-spaced wires on the sheet, and each wire is infinitely long. Using symmetry and Ampere's law, find the magnitude and direction of the magnetic field at a point a distance D above the sheet. For the purposes of this problem, use a coordinate system such that the infinite sheet lies in the x-y plane with the current flowing in the +x-direction. The z-axis is perpendicular to the sheet, as shown. Top view Cross-sectional view TO

PROBLEM 1. As shown in the figure, a uniform magnetic field B points upward, in the plane of the paper. Then the current is turned on in a long wire perpendicular to the paper. The magnetic field at point 1 is then found to be zero. From this information, draw the magnetic field vector at point 2 when the current is on. Draw the vector starting at the black dot. The location and orientation of the vector will be graded. The length of the vector will not be graded. Explain your reasoning. 2• H Wire 1.

A long, cylindrical conductor of radius R carries a current I as shown in the figure below. The current density J, however, is not uniform over the cross-section of the conductor but is a function of the radius according to J = 2br, where b is a constant? Find an expression for the magnetic field magnitude B at the following distances, measured from the axis. (Use the following variables as necessary: ?0, r1, r2, b, R.) (a) r1 < R (b) r2 > R

A rectangular wire loop of height h, width w, and net electrical resistance R lies in the x-y plane. As shown in the figure below, the entire region x < 0 of space is occupied by a constant, uniform magnetic field which points in the –z direction (into the page). In order to determine the magnitude of this field, a student pulls the wire loop out of the magnetic field region at a constant velocity v in the +x-direction, and measures the current I induced in the loop during this process. I = 17 μAR = 35 ohmsh = 3 cm w = 8 cmv = 2 cm/sec a) What is the direction of the current induced in the wire loop? b)What is the magnitude B of the magnetic field?