Magnitude, 2D co-ordinates and Coulomb's Law

[Mary O'Donovzn]

Homework Statement

How do you calculate compute the the magnitude of the total force of three charges and also the angle it makes with the x-axis? Knowing the magnitude and also the 2d co ordinates of the charges. (x1,y1) (x2,y2) (x3,y3)

I know for definite I use the below calculation but what exactly is r hat?
K0 * Q1.Q2 / d^2 * r hat

there is apparently 2 thetas aswell.

Homework Equations

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K0 * Q1.Q2 / d^2 * r hat

r hat = cos(theta)i + sin(theta)j
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^I have no idea how to get this with 2D coordinates

The Attempt at a Solution

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In my attempt at a solution I subbed in K0=8.9875 * 10^9

I subbed in Q1Q2 (F12)
I subbed in Q1Q3 (F13)
I subbed in Q2Q3 (F23)

Then for each of them I used the x and y co ordinates of them,.
Then I got 100 % confused by r hat :(

I appreciate any help at all

Thanks in advance :)

 

[spl-083902]

r-hat (\hat{r}) is a unit vector. Unit vectors have a length of 1. In this way you can separate out the "magnitude" of a vector from its direction. So you can think of r-hat as a vector (of length 1) that points in the direction from the particle to where you want to measure the force at.
Any vector can be expressed as the product of a magnitude and a unit vector, like: R\hat{r} where R is the magnitude (length) of the vector and \hat{r} is the direction.

So in your equation: K0 * Q1.Q2 / d^2 * r hat
(K0 * Q1.Q2 / d^2) is the magnitude and r hat is the direction.

In the equation:
r hat = cos(theta)i + sin(theta)j
'j' and 'i' are also unit vectors: i=(1,0) j=(0,1)