Electric potential of 3 point charges

[benchwarmer08]

Homework Statement

Three point charges, which initially are infinitely far apart, are placed at the corners of an equilateral triangle with sides "b". Two of the point charges are identical and have charge "q".

If zero net work is required to place the three charges at the corners of the triangle, what must the value of the third charge be?

Homework Equations

The Attempt at a Solution

I know the electric potential at infinity is zero, but I'm not sure how to start this

 

[vorcil]

Don't forget about conservation of energy, The final potential energy between each of the charges is the some of the potential energy between them,

You are given this information:
1:Three charges are set up in a triangle
2:Two of the charges have charge q
3:The net potential is ZERO

what does super position say?
the sum of the charge is,

q1+q2+q3=0

what happens to that equation when q1 and q2 are the same?

solve that for q3, the charge on the other charge

 

[nickjer]

What vorcil originally said is correct. The final potential energy is the sum of the potential energy between each pair of charges. But that isn't the same as the sum of the charges (not sure where that came from).

I suggest first writing out the potential energy equation and showing some work benchwarmer. And we can help you from there.

 

[benchwarmer08]

I figured it out guys, thanks

 

[paranormal]

problem.

I would approach this problem by first considering the concept of electric potential. Electric potential is a measure of the potential energy of a point charge in an electric field. It is defined as the amount of work that must be done to bring a unit positive charge from infinity to a specific point in the electric field.

In this problem, we are given that the net work required to place the three charges at the corners of the equilateral triangle is zero. This means that the total electric potential of the three charges at the corners must also be zero.

We can use the formula for electric potential, V = kq/r, where k is the Coulomb's constant, q is the charge, and r is the distance from the point charge to the specific point. In this case, we can consider the point at infinity as our reference point with a potential of zero.

Since two of the point charges are identical and have the same charge, their electric potentials at the corners of the triangle will cancel each other out, resulting in a net potential of zero. Therefore, the remaining point charge must have an opposite charge to balance out the potential and make it zero.

To determine the value of the third charge, we can use the formula for the electric potential of a point charge, V = kq/r, and set it equal to zero. Solving for q, we get q = -k/br. This means that the third charge must have a charge of -k/br in order for the net electric potential of the three charges at the corners of the triangle to be zero.

In conclusion, the value of the third charge must be -k/br in order for the net electric potential of the three charges at the corners of the equilateral triangle to be zero.