Electric Potential Problem Assistance

[phunphysics1]

Electric Potential Problem Assistance!

Homework Statement

There is an equilateral triangle with one point charge at each vertex. The point charges have charges of -Q, +3Q and -4Q respectively. The length of one side of the triangle is L. Determine an expression in simplest form for the electric potential at a point halfway between the -Q and +3Q point charges. Simplest form means that the answer is factored completely and consists of only one simple fraction.

Homework Equations

V=kQ/r
Vtot=V_1+V_2+V_3

The Attempt at a Solution

I tried to solve for each missing length "L" I figured that between charges -Q and +3Q it was L/2 because we are looking at a point halfway between them. But I am confuse how to show this through individual calculation of electric potential because L is a variable??

 

[diazona]

Why are you solving for L?

L is a given quantity, the length of a side of the triangle. In a real situation, it would be something that you would measure, perhaps 3 cm, or 10 cm, or 5 m, and you would plug that number in wherever you needed the side length of the triangle. But pretend that you don't have a ruler, so you can't measure exactly how large the triangle is. You're just using a letter to stand in for that length, so that later on, when you do measure it, you'll know where to plug it into the formula.

Anyway, back to the problem: you are trying to find the total electric potential at a certain point.
1. What is the potential produced by one of the charges at the point?
2. What is the potential produced by another of the charges at the point?
3. What is the potential produced by the remaining charge at the point?
4. How do you find the total potential?

 

[phunphysics1]

I thought that I was solving for L, in order to find the potential v for each charge at that point? So then what am I solving for if that is not the case?? It doesn't want a numerical number as the value, just variables??

 

[iratern]

No, the question doesn't want a numerical value.

A tip: The answer is in terms of L and Q. The simplest form would include them and a rational number.

 

[rwisz]

The electric potential at a point halfway between two point charges can be calculated by using the equation V=kQ/r, where k is the Coulomb's constant, Q is the charge of the point charge, and r is the distance between the point charge and the point where the potential is being calculated.

In this case, the distance between the -Q and +3Q point charges is L/2, as you correctly identified. So, the electric potential at this point can be calculated as:

V_1 = k(-Q)/(L/2) = -2kQ/L

V_2 = k(3Q)/(L/2) = 6kQ/L

Since the potential at a point is the sum of the individual potentials due to each point charge, the total potential at this point is:

Vtot = V_1 + V_2 = -2kQ/L + 6kQ/L = 4kQ/L

Therefore, the expression for the electric potential at a point halfway between the -Q and +3Q point charges is 4kQ/L, which is already in its simplest form since it cannot be factored any further.