For unlimited access to Homework Help, a Homework+ subscription is required.
You are given a hollow copper cylinder with inner radius a and outer radius 3a. The cylinder's length is 200a and its electrical resistance to current flowing down its length is R. To test its suitability for use in a circuit, you connect the ends of the cylinder to a voltage source, causing a current I to flow down the length of the cylinder. The current is spread uniformly over the cylinder's cross-section. You are interested in knowing the strength of the magnetic field that the current produces within the solid part of the cylinder, at a radius 2a from the cylinder axis. But since it's not easy to insert a magnetic-field probe into the solid metal, you decide instead to measure the field at a point outside the cylinder where the field should be as strong as at radius 2a. At what distance from the axis of the cylinder should you place the probe?
The attached figure shows the electric field inside a cylinder of radius R=3.0mm. The field strength is increasing with time as E = 1.0x10^8 t^2 V/m (where 't' is in seconds). The electric field outside the cylinder is always zero, and the field inside the cylinder was zero for t < 0.
a: Find an expression for the electric flux through the entire cylinder, as a function of time.
b: Find an expression for the magnetic field strength as a function of time, at a distance r<R from the center.
c: Find an expression for the magnetic field strength as a function of time, at a distance r>R from the center.
d: Draw a picture showing the magnetic field lines inside AND outside the cylinder.
An electric current is flowing through a long cylindrical conductor with radius a = 0.15 m. The current density J= 5.5 A/m2 uniform in the cylinder. In this problem, we consider an imaginary cylinder with radius r around the axis AB
(a) When r is less than a, express the current inside the imaginary cylinder ir in terms of r and J.
(b) Express the magnitude of the magnetic field B at r in terms of the current through the imaginary cylinder ir and its radius.
(c) For r = 0.5 a. calculate the numerical value of B in Tesla