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Given that $$H = \pm \frac{I}{2}\frac{\partial}{\partial x}(\frac{x}{\sqrt{r^2+x^2}})$$

I need to prove that $$H = \pm \frac{r^2I}{2\sqrt{(r^2+x^2)^3}}$$ where $H$ is the magnetic field vector due to a steady current $I$ flowing around a circular wire of radius $r$ and at a distance $x$ from its centre.

I could manage to partially differentiate $\frac{\partial}{\partial x}(\frac{x}{\sqrt{r^2+x^2}}) = \sqrt{r^2+x^2}-x^2$ after using the quotient rule and a little bit of simplification.

Please help as I am unable to prove the above expression.

Thank You.

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Your derivative is wrong, the result should be just $r^2/(r^2+x^2)^{3/2}$. – enzotib Aug 23 '12 at 9:32
Ah yes.Now i get it.Thank You very much. – alok Aug 23 '12 at 9:39
@enzotib Would you post that as an answer? – process91 Aug 23 '12 at 15:43

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