Question

Constants Part A 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? Express your answer in terms of a and I Submit Request Answer

Answer 1

Part A )

using Apmere's Law

$\int B dl = \mu_o I$

$B ( 2\pi (2a)) = \mu_o I_i$

then the inside current is

$I_i = I \left(\frac{(2a)^2-a^2}{(3a)^2-a^2} \right )$

I_i = 3 I / 8

the magnetic field is

B = 3 $\mu$_o I / 16 x 2$\pi$ a

and the magnetic field is

B = $\mu$_o I / 2$\pi$

1/r = 3 / 16a

r = 16 a / 3