Solving Biot Savart Law Homework: Infinitely Long Wire

[mastertan]

Homework Statement

Using the Biot Savart Law

dB = (u0*i*ds X r)/(4*pi*r^3)

*X is cross product

show that the magnetic field due to an infinitely long straight wire carrying a current i ampere is given by

B = (u0*i)/(2*pi*r)

Homework Equations

Hint: integral (Rds/(s^2+R^2)^3/2) = s/(R*(s^2+R^2)^1/2)

The Attempt at a Solution

Eventually I got something like

B = (i*u0*s)/(4pi*R*(s^2+R^2)^1/2)

which I am pretty sure is correct,
but I don't know how to make that equation become

B = (u0*i)/(2*pi*R)

Any ideas? (I hope the question and all the equations make sense)
Thanks

 

[vela]

Did you plug the limits of the integral in?

 

[mastertan]

I haven't put in the limits. I wasn't too sure what to do.

 

[vela]

What are the limits on your integral?

 

[mastertan]

Is it -infinite and +infinite?

 

[vela]

Yes. You're told the wire is infinitely long, so s runs from -∞ to +∞, so your expression for B should be

$$B = \left.\frac{i \mu_0 s}{4\pi r\sqrt{s^2+r^2}}\right|_{-\infty}^\infty \equiv \lim_{a\to\infty} \left.\frac{i \mu_0 s}{4\pi r\sqrt{s^2+r^2}}\right|_{-a}^a$$

 

[mastertan]

Ah I get it now. Thanks very much for helping me out.