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## Homework Statement

A 100 nC point charge is located at A(-1, 1, 3) in free space. (a) Find the locus of all point P(x,y,z) at which [itex]E_x = \frac{V}{m}.[/itex] Find [itex]y_1[/itex] if P(-2,[itex]y_1,3[/itex]) lies on that locus.

## Homework Equations

[itex]E=k\frac{q}{r^2}\vec{r}\hspace{10pt}E_X=E\cos\theta\hspace{10pt}\vec{R}=<(x_2-x_1),(y_2-y_1),(z_2-z_1)>\hspace{10pt}[/itex]

Cartesian to Spherical: [itex]r=\sqrt{x^2+y^2+z^2}\hspace{10pt}\theta = cos^{-1}\frac{z}{\sqrt{x^2+y^2+z^2}} \hspace{10pt} \phi = \cot^{-1}\frac{x}{y}[/itex]

## The Attempt at a Solution

I converted the vector R to spherical coordinates because I figured that using the radius I could find the field where [itex]\theta[/itex] and [itex]\phi = 0[/itex] then convert back to cartesian...It didn't work. I had a hint that I should use [itex]E=k\frac{q}{\vert{\vec{R}\vert^3}}\vec{R}[/itex] but I don't quite understand why. I believe this is just multiplying by 1, but I thought that while [itex]k\frac{q}{r^2}\vec{r}[/itex] already include the vector I could just plug in [itex]\vec{R}[/itex] for unit vector [itex]\vec{r}[/itex] then why would I have to divide by the magnitude again.

I am sure at this point that I am misunderstanding things so any clarification of these concepts it priceless. Thanks in advance for any tips.