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Calculate the Electric Field at the given point

  1. Sep 27, 2014 #1
    1. The problem statement, all variables and given/known data
    A -12 nC charge is located at the origin.

    What is the electric field at the position (x2,y2)=(−5.0cm,−5.0cm)? Write electric field vector in component form.
    2. Relevant equations
    upload_2014-9-27_11-44-48.png

    3. The attempt at a solution
    Here, r^2 = (-0.05 - 0 )^2 meters squared. q=-12*10^-9 C.
    For the unit vector, I chose \hat{i} and \hat{j} for the horizontal and vertical components of the vector. In the solutions manual, they choose a unit vector \frac {1} {\sqrt{2}}. I am not sure how they chose this as their unit vector.

    I think they start with unit vectors of 5*\hat{i} and 5*\hat{j} then to convert to unit vectors they divide by the magnitude of each of the vectors (which is the length of the hypotenuse; 5*\sqrt(2).

    Can someone verify this, please?
     

    Attached Files:

  2. jcsd
  3. Sep 27, 2014 #2

    Orodruin

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    The point is that ##\hat r## should be a unit vector with the same direction as ##\vec r##. The vector ##\vec a = \hat i + \hat j##, this is not a unit vector since ##\vec a^2 = 2##. Additionally, ##\hat r## should be pointing away from the origin, which in (-5cm, -5cm) means that it is given by ##- \frac 1{\sqrt 2}(\hat i + \hat j)##.
     
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