Electric Field Direction at Origin: Cancel or Enhance on x-axis?

[acherentia]

Homework Statement

three equal and positive charges q are located equidistant from the origin as shown http://s966.photobucket.com/albums/ae146/acherentia/?action=view&current=directionofanelectricfield.jpg . Is the direction of the electric field at the origin a) along x, b)along -x, c) along +y d) along -y

Homework Equations

The electric field is directed outward away from Q when Q is positive.

The Attempt at a Solution

Do the field lines along the x-axis emerging from the charges on the x-axis cancel or enhance each other at the origin?

Do I have to do vector addition on the x-axis to solve this problem?

 

[berkeman]

Homework Statement

three equal and positive charges q are located equidistant from the origin as shown http://s966.photobucket.com/albums/ae146/acherentia/?action=view&current=directionofanelectricfield.jpg . Is the direction of the electric field at the origin a) along x, b)along -x, c) along +y d) along -y

Homework Equations

The electric field is directed outward away from Q when Q is positive.

The Attempt at a Solution

Do the field lines along the x-axis emerging from the charges on the x-axis cancel or enhance each other at the origin?

Do I have to do vector addition on the x-axis to solve this problem?

Just do the vector addition at the origin. What are the 3 E-field vectors at the origin? (magnitudes and directions)

 

[acherentia]

for the charge on the -x axis : kQ/r^3 x r_i
for the charge on the +x axis: kQ/r^3 x r_-i
for the charge on the +y axis: kQ/r^3 x r_-j

so the charges that are sitting on the x-axis will cancel out. how do i write that in a more mathematical way?

 

[berkeman]

for the charge on the -x axis : kQ/r^3 x r_i
for the charge on the +x axis: kQ/r^3 x r_-i
for the charge on the +y axis: kQ/r^3 x r_-j

so the charges that are sitting on the x-axis will cancel out. how do i write that in a more mathematical way?

Correct. In general, you would write the vector sum in rectangular coordinates. Express each individual vector as the sum of its x and y components (using the i,j vector notation, or x-hat, y-hat, etc.), and show the sum of them as a sum of x components and y components, still in rectangular vector notation.

And in this problem, it's just multiple choice anyway. Which is your answer?

 

[acherentia]

The answer is d, along -y

 

[berkeman]

The answer is d, along -y

Yep. Good work.