How Do You Calculate the Magnetic Field in a Cylindrical Conductor?

[wisper]

A conductor is made in the form of a hollow cylinder with inner and outer radii a and b, respectively. It carries a current I, uniformly distributed over its cross section.

Derive an expression for the magnitude of the magnetic field in the region a < r < b.

I understand that it needs to relate to the following equation but that is it. $$B=\frac{\mu_{0} I}{2\Pi r}$$

I am unsure how to derive an answer for this, I am drawing a blank on solving this. Can anyone give me any helpful hints?

 

[vincentchan]

what is the direction of the current? post the whole question pls...

 

[wisper]

That is the full question, the current is running through a hollow cylinder. From how I understand the current is flowing through direction of the hieght of the cylinder.

 

[vincentchan]

find the $\ver{A}$ first, then B

 

[clive]

$$\oint{\vec{B}\vec{dl}}=\mu_0\int{\int_S{j}}ds$$
and from this you can simply derive

$$B(r)2\pi r=\mu_0 j \cdot \pi(r^2-a^2)$$

where
$$j=\frac{I}{\pi (b^2-a^2)}$$.

 

[wisper]

Thanks to both of you. Clive you pointed out a part in which I made an error in my thinking of my previous answer. Appreciate the help.