Biot-Savart Law (infinite filament)

[gsan]

An infinite current filament carries a current of 3A and lies along the x-axis. Using Biot-Savart Law, find the magnectic field intensity in cartesian coordinates at a point P(-1,3,2).

dH = I vec{dl} x hat{R} / 4piR^2

let substitude hat{R} with vec{R} / R

then dH = I vec{dl} x vec{R} / 4piR^3

vec{R} = hat{x}(-1-x) + hat{y}3 + hat{z}2 and vec{dl} = hat{x}dx

vec{dl} x vec{R} =
|hat{x} hat{y} hat{z}|
| 1 0 0 |
| (-1-x) 3 2 |

=[hat{y}-2 + hat{z}3] dx

dH = (I)(dx)(hat{y}-2 + hat{z}3) / 4piR^3

magnitude of R = sqrt [(-1-x)^2 + 3^2 + 2^2]

dH = (I)(dx)(hat{y}-2 + hat{z}3) / 4pi[(-1-x)^2 + 3^2 + 2^2]^3/2

how do I solve for the next step? thanks!

 

[nasu]

You should integrate each component of the field.

 

[gsan]

I don't know how to integral since it is very complicated.