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Point charge 3.5μC is located at x = 0, y = 0.30 m, point charge -3.5μC is located at x = 0 y = -0.30 m. What are (a)the magnitude and (b)direction of the total electric force that these charges exert on a third point charge Q = 5.0μC at x = 0.40 m, y = 0?

Charges

I first drew a diagram, showing that it can be broken down into two .3, .4, .5 triangles, leaving me with a theta of 36.87°. I then calculated that because the charges are equal, each individual force enacted on charge Q is .63N. I know I need to split the force into it's x and y components to find the resultant vector using R=√Rx^2 + Ry^2, but I do not know how to split these forces up.

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  • $\begingroup$ I see that the resultant will be going straight down now, but how do I calculate the x component of each force to find the magnitude of the force on Q? $\endgroup$
    – Cre
    Sep 2 '14 at 7:03
  • $\begingroup$ Be careful, the charges are equal in magnitude but opposite in sign. This means that the force will change directions as well (as is indicated by the direction of the arrows in your diagram). $\endgroup$
    – Bryson S.
    Oct 3 '14 at 16:42
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Here is a big hint... I have to believe you can finish it from here. The key is "similar triangles".

enter image description here

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  • $\begingroup$ In particular note that $\sin\theta = 0.3/0.5$ $\endgroup$ Sep 2 '14 at 7:26
  • $\begingroup$ I see that theta will be equal to 36.87°. How can I find the magnitude of the force with this information without splitting the .63N into it's y components though? It seems like your solution would only tell me how far the particle would travel. $\endgroup$
    – Cre
    Sep 2 '14 at 7:31
  • $\begingroup$ From the similar triangle I drew, you can see the vertical component is 3/5 of the total vector. You never need to know the actual angle. This is also what John Rennie was hinting at. So with two of these, the total downward force is 2*3/5 of the force of one of the 3.5 uC charges on the 5 uC charge. $\endgroup$
    – Floris
    Sep 2 '14 at 7:46
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I found the answer to be .756N by multiplying .63N and sin(36.87).

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