- #1
latentcorpse
- 1,444
- 0
we have [itex]\mathbf{A(r)}=\frac{\mu_0 I}{4 \pi} \int dV' \mathbf{\frac{dl'}{|r-r'|}}[/itex]
i need to show that [itex]A_x=-\frac{\mu_0 I}{4 \pi} \int_{-x}^x \frac{d \xi}{(\xi^2 + y^2 + z^2)^{-\frac{1}{2}}}[/itex]
i said [itex]|\mathbf{r-r'}|=\sqrt{(x-x')^2+(y-y')^2+(z-z')^2}[/itex]
then if we pick [itex]\mathbf{r'}[/itex] on the x axis, y'=z'=0
then we let [itex]\xi=x-x' \Rightarrow dl'=-d \xi[/itex]
so everything's looking good up till now but i can't get the limits on the integration to come out right.
x' goes between [itex]-\infty[/itex] and [itex]+\infty[/itex] btw
any ideas?
i need to show that [itex]A_x=-\frac{\mu_0 I}{4 \pi} \int_{-x}^x \frac{d \xi}{(\xi^2 + y^2 + z^2)^{-\frac{1}{2}}}[/itex]
i said [itex]|\mathbf{r-r'}|=\sqrt{(x-x')^2+(y-y')^2+(z-z')^2}[/itex]
then if we pick [itex]\mathbf{r'}[/itex] on the x axis, y'=z'=0
then we let [itex]\xi=x-x' \Rightarrow dl'=-d \xi[/itex]
so everything's looking good up till now but i can't get the limits on the integration to come out right.
x' goes between [itex]-\infty[/itex] and [itex]+\infty[/itex] btw
any ideas?