Question

Linear algebra + calculus. Question below.

Answer 1

This is originally a physics question but I have the physics part pretty much done and get stuck while trying to integrate, so I thought it might be more apropriate in the maths forum.

Use Biot-Savart law to calculate the magnetic field in a single point above a straight finite conductor.

From Biot-Savart law we get
\[\large B = \oint_{L} \frac{ \mu_0 I \space dl \times \hat{r} }{ 4\pi r^2 }\]\[\large = \frac{ \mu_0 I }{ 4 \pi } \int\limits_{-L}^{L} \frac{ \hat{z} \times (-z \space

\hat{z} + R \space \hat{R}) }{ (z^2+ R^2)^{3/2} }dz = \frac{ \mu_0 I }{ 4 \pi } \int\limits_{-L}^{L} \frac{ R \hat{\phi} }{ (z^2+ R^2)^{3/2} }dz\]\[\large = \frac{ \mu_0 I

}{ 4 \pi } R \hat{\phi} \int\limits_{-L}^{L} u^{-3/2}dz \]\[\large u = z^2 + R^2 \rightarrow du = 2z \space dz\]It was some time since I did calculus and from what I remember the substitution isn't going to work(?). It's possible to solve using Wolfram but I need to be able to do this on the exam.

Any ideas on how to continue?

Answer 2

http://www.brainfuse.com/highed/helpNow.asp?a_id=F63A9782&ss=&r=

Answer 3

this one is not a nce integral but u didnt sub for dz interms of du and ucan writ z interms of u see what that does