- #1

JJBladester

Gold Member

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## Homework Statement

A -10.0 nC charge is located at position (x,y) = (2.0cm, 1.0cm). At what (x,y) position(s) is the electric field:

161,000i - 80,500j N/C

x = ??? cm

y = ??? cm

## Homework Equations

E = Kq/r

^{2}

## The Attempt at a Solution

I know that the magnitude of E is [tex]\sqrt{161,000^{2}+80,500^{2}}[/tex] = 1.8e

^{5}.

So, to find the distance between the electric charge and where the field is:

1.8e

^{5}= Kq/r

^{2}

Therefore, r = [tex]\sqrt{(9e^{9})(10e^{-9})/1.8e^{5}}[/tex] = .02m = 2cm

So, I know the distance between the charge and the electric field. The angle that the electric field makes with the x-axis is tan

^{-1}(-80,500/161,000) = -26.57

I was thinking that I have to do something with polar coordinates to finish the problem but I can't seem to make the mental leap.

I know in polar coordinates, if you're given a distance (2cm) and an angle (-26.57), you should be able to find the rectangular coordinates by:

x = 2cos(-26.57)

y = 2sin(-26.57)

But isn't this the position of the electric field in relation to the origin (not the charge)?