- #1

TW Cantor

- 54

- 1

## Homework Statement

An electric charge e which moves through a material of permeability μ with a velocity v, produces a magnetic field β at a point r given by:

β= ((μ*e)/(4*∏))*((v*r

_{u})/(|r|)

^{2})

where r

_{u}is a unit vector in the direction of r.

Find β if v=4i+3j+3k and r=4i+7j+5k.

Take μ=e=93 in appropriate units.

## Homework Equations

equation for a unit vector: (a*b)=(a

_{2}*b

_{3}-a

_{3}*b

_{2})i-(a

_{1}*b

_{3}-a

_{3}*b

_{1})j-(a

_{1}*b

_{2}-a

_{2}*b

_{1})k

## The Attempt at a Solution

so i know μ .and e are both = 93 so i know that:

(μ*e)/(4*∏) is going to be a constant. i worked it out to be 688.266

i worked out |r|

^{2}:

4

^{2}+7

^{2}+5

^{2}=90

then i tried to use the equation for a unit vector to calculate r

_{u}. this gave me:

r

_{u}= -48.902i + 0.060j - 65.143k

i then put all these values back into the original equation and it came out with:

β = -373.973i + 0.459j - 498.174k

when the actual answer is:

β = -4.836i - 6.448j + 12.897k

can anyone help me find what i have done wrong?