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

  1. Oct 20, 2014 #1
    1. The problem statement, all variables and given/known data

    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.

    2. Relevant equations

    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

    3. The attempt at a solution

    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 :)
     
  2. jcsd
  3. Oct 20, 2014 #2
    r-hat ([itex]\hat{r}[/itex]) 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: [itex]R\hat{r}[/itex] where R is the magnitude (length) of the vector and [itex]\hat{r}[/itex] 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)
     
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