A point charge +2Q is at the origin and a point charge −Q is located along the x axis at

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A point charge +2Q is at the origin and a point charge −Q is located along the x axis at

x = d as in the figure below. Find a symbolic expression for the net force on a third point charge +Q located along the y axis at y = d. (Use the following as necessary: ke, the Coulomb constant, Q, and d.)
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asked Jan 15, 2012 in Physics by Joey33 ~Expert~ (1,216 points)
    

1 Answer

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Best answer

So you are finding the forces acting on the third charge, for simplicity we'll call it Q3, and the one below it will be Q1, and the negative Q we'll call Q2.

So the formula states that:

Forces acting on Q3 = Force of Q1 on Q3 + Force of Q2 on Q3 or simply:

F3 = F13 + F23

 

Now just calculate F13 and F23.

The formula for electric force is as follows:


F=(ke * q1*q2)/ r^2

and r is the distance between the two charges.

you will find r for each equation by looking at the diagram.

First lets find F13, which plugging into the equation we get that:

F13 = (ke*2Q^2)/d^2

Now to find F23 is a little trickier and requires breaking down the force into its x and y components.

Lets first find F23(x-component) = (ke*Q^2)(cos45) / (2d^2)  (this is found based on the geometry of the triangle)

and similarly F23(y-component) = (ke*Q^2)(sin45) / (2d^2)

Now add the 2 forces, (remember that F13 only has the y-component):

F3 = [(ke*Q^2)(cos45) / (2d^2)] i + [(ke*2Q^2)/d^2 - (ke*Q^2)(sin45) / (2d^2)] j

this can be further simplified to:

F3 = (ke*Q^2) / d^2 [ 1/(2*2^(1/2)) i + (2 - 1/(2*2^(1/2)) j ]  

*note the i and j are there to represent the vector components of the force.

 

answered Jan 19, 2012 by kirby ~Expert~ (3,020 points)
selected Jan 19, 2012 by Joey33



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