Solving Biot Savart Law Homework: Infinitely Long Wire

AI Thread Summary
The discussion focuses on using the Biot-Savart Law to derive the magnetic field around an infinitely long straight wire carrying a current. The initial equation derived was B = (i*u0*s)/(4pi*R*(s^2+R^2)^(1/2)), but the goal is to simplify it to B = (u0*i)/(2*pi*R). Participants clarify that the limits of integration should be from -∞ to +∞, which is crucial for the derivation. This leads to the realization that plugging in these limits correctly will yield the desired result. The conversation emphasizes the importance of understanding the integral limits in solving the problem.
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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
 
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Did you plug the limits of the integral in?
 
I haven't put in the limits. I wasn't too sure what to do.
 
What are the limits on your integral?
 
Is it -infinite and +infinite?
 
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
 
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Ah I get it now. Thanks very much for helping me out.
 
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