Chapt. 30 Currents Causing Magnetic Fields 231 b) Imagine that you superimpose another cylindrical conductor of radius b on the ±rst. The two cylinders have aligned symmetry axes. The second cylinder has current − v J with direction aligned with the symmetry axis. The second cylinder is smaller than the ±rst cylinder and entirely inside it, but o²-center by an amount c : i.e., c is the distance from the center of the ±rst cylinder to the center of the superimposed one. What is the magnetic ±eld at the center of second cylinder due to its own current only? What is the net magnetic ±eld at the center of second cylinder? What is net current density inside the second cylinder? HINT: Draw a diagram. c) What is the net magnetic ±eld inside the second cylinder at any point along the line from the center of the ±rst cylinder and passing through the second cylinder’s center? Be very careful about getting the signs of the components correct.
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