Biot-Savart Law (infinite filament)

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To find the magnetic field intensity at point P(-1,3,2) using the Biot-Savart Law, the equation dH = I vec{dl} x vec{R} / 4piR^3 is established, where vec{R} is defined in terms of the coordinates. The cross product of vec{dl} and vec{R} yields components in the y and z directions. The magnitude of R is calculated using the distance formula, leading to a complex expression for dH. To proceed, the next step involves integrating each component of the magnetic field, although the integration process is noted to be complicated. The discussion highlights the need for assistance in performing these integrations.
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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!
 
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You should integrate each component of the field.
 
I don't know how to integral since it is very complicated.
 
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