- #1

Stendhal

- 24

- 1

## Homework Statement

A long, straight wire lies along the z−axis and carries a 4.20 −A current in the +z−direction. Find the magnetic field (magnitude and direction) produced at the following points by a 0.400 −mm segment of the wire centered at the origin.

## Homework Equations

## \vec B ## = 2 ## \frac {μ_0} {4π} ## ## \int_0^.0004 ## ## \frac {I*d\vec s \times \hat r} {r^2}##

x = 2 meters, y = 2meters, z=0

## d\vec s \times \hat r ## = ds*sin(Θ)

## The Attempt at a Solution

I took the original equation, which is from the Biot-Savart Law, and simplified the cross product using the algebraic definition above, such that the problem simplifies into:

## \vec B ## = 2 ## \frac {μ_0 I} {4π} ## ## \int_0^.0004 ## ## \frac {ds*sin(Θ)} {r^2}##

Where the angle is that between the z-axis and the hypotenuse, such that sin(Θ) can be described as:

sin(Θ) = ##\frac {\sqrt (x^2+y^2)} {r}##

which gives

## \vec B ## = 2 ## \frac {μ_0 I \sqrt(8)} {4π} ## ## \int_0^.0004 ## ## \frac {ds} {\sqrt(s^2 +2^2 +2^2)^3}##

Which, when I solve gives me the answer for the magnitude and direction of the magnetic field of

##8.4*10^{-15} T## which doesn't seem right at all, since previous answers to some other parts of this problem were in around ^-11. Any help is greatly appreciated!