A steady current I flows down a long cylindrical wire of radius a. Find the magnetic field both inside and outside if, a) The current is uniformly distributed over the outside surface of the wire. b) The current is distributed in such a way that J is proportional to s, the distance from the axis.

This is a practice problem from the Engineering Electromagnetics course in my Electrical Engineering program. Could you please walk me through the steps of solving it so that I can solve more complicated ones in the future? Thank you for your assistance.

A wire carrying a current /= 27.0 A is bent into the shape of an exponential spiral. Its polar coordinate is described by r = exp(0) from 0-0 to 0-2 as shown in the figure. dr ds B-x/4 To complete the loop, the ends of the spiral are connected by a straight wire along the x axis. Find the magnitude of the magnetic field B at the origin. Suggestions: Although this problem may look daunting at first, remember that the Biot-Savart law is a good starting point to find the magnetic field due to a given current distribution. The simple exponential dependence of the path on the angle should give rise to an integral that is easy to solve. Also, it may help to know that the angle ẞ between a radial line and its tangent line at any point on the curve r = f(0) is related to the function in the following way: tan(B) dr di Thus, in the case of r = exp(0), tan(B)=1 and ẞ=4. Therefore, the angle between the line element vector ds and the radial unit vector r^ is -ẞ=. Additionally, this gives: dr…

An infinitely-long, hollow, conducting cylinder carries a uniform current I that flows parallel to its axis and into the paper. Its inner radius is a and its outer radius is b. Derive expressions for the magnetic field for (a) a < r < b and (b) r > b Note: See image for the figure.