(i)Show that the magnetic field [latex]\mathbf{B}[/latex] on the axis

[xboy]

Substitute that in your original expression and see. Incidentally you won't get back the original term ( the first expression you wrote) but the modified term for z tending to infinity. This is because you've calculated the field using that condition.

 

[latentcorpse]

$B(z)=\frac{1}{2} \mu_0 \sigma \omega \frac{r^3 dr}{z^3}$ as b-> a dr->0 though?

 

[xboy]

That's what you should get.

 

[latentcorpse]

hmmm...surely if dr->0, then B(z)->0 which doesn't make much sense though?

 

[xboy]

You should try to work out an expression for the current through this ring.