Snagged a little on some vector math

Thread starter whiterabbit9
Start date Feb 2, 2012
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Vector

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The radial unit vector is defined as \(\hat{r} = \vec{r}/r\), where \(\vec{r}\) is the position vector and \(r\) is its magnitude. In Cartesian coordinates, \(\hat{r} = (x/r, y/r, z/r)\) with \(r = \sqrt{x^2 + y^2 + z^2}\). When using only one component, such as \(\hat{r}_x\), it simplifies to \(\hat{r}_x = x/r\). This approach helps in calculating electric fields by providing directionality based on the position in space. Understanding this algebra is crucial for accurately determining electric field vectors in physics.

Feb 2, 2012

whiterabbit9

I'm learning how to calculate E-fields and, in some examples, when using the unit vector r^ with only one component (ie r^x or r^y), it is simply defined r^x=x/r. I am missing the algebra. Will anyone explain this to me? Thanks

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Feb 2, 2012

vanhees71

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Bei definition the radial unit vector ist \hat{r}=\vec{r}/r. In Cartesian coordinates, you have \hat{r}=(x/r,y/r,z/r) with r=\sqrt{x^2+y^2+z^2}.

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