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

+4 votes

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.)
net =

asked Jan 15, 2012 in Physics

## 1 Answer

+3 votes

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

## Related questions

–2 votes
1 answer 277 views
277 views
0 votes
0 answers 12 views
12 views
+4 votes
1 answer 4,034 views
4,034 views
+7 votes
2 answers 3,946 views
3,946 views
+5 votes
1 answer 4,388 views
4,388 views