Question

please show neat work

[12] 14. The figure shows a cross section of a 200 m long solid cylindrical conductor whose radius is 26.8 cm. It carries a uniform current of 750 A. Using Ampere's Law, determine the magnetic field at a distance of 11.0 cm from the center. Hint: You need to calculate the current density to help you solve the problem. If you show your work in an organized, and clear manner that I can see that you are working the problem correctly and not just writing from the memory of some problem that was previously worked out, you will get partial credit depending, on how correct you work is. Direction: Answer: (Magnitude)

Answer 1

The current density of the wire is the current per unit area i.e.,

J = 2

R is the radius of the conducting wire.

We need to find the magnetic field at a distance r=11 cm=0.11 m from the center of the wire

By Ampere's circuital law magnetic field is given by

$\int B.dl=\mu_0I_{enc}$

I_enc is the current enclosed.

We need to find the magnetic field at a distance r<R of the wire.

So, we have

$\int B.dl=\mu_0J\times\pi r^2$

$or,\ B.2\pi r=\mu_0\times\frac{I}{\pi R^2}\times\pi r^2$

$or,\ B=\frac{\mu_0}{2\pi}\frac{Ir}{ R^2}$

$=\frac{4\pi\times10^{-7}}{2\pi}\times\frac{750\times0.11}{0.268^2}\ T$

$=2.3\times10^{-4}\ T$

This is the required magnetic field.

Direction of magnetic field can be determine using the right hand thumb rule. Assuming the current is directed towards us the magnetic field is anticlockwise.