Electric Potential Due to point charges

[MidgetDwarf]

Homework Statement

1. Two particles each with a charge of +3.00 μC are located on the x axis, with one particle at x = -0.80 m, and the other particle at x = +0.80 m.
   
   1. a) Determine the electric potential on the y-axis at the point y = 0.60 m.
      
      
   2. b) What is the change in electric potential energy of the system if a third particle of charge
      
      q = - 3.00 μC is brought from infinity to the point on the y-axis where y = 0.60 m?
      

Homework Equations

Vp=KQ/r
Vb-Va
Pythagoras Theorem

The Attempt at a Solution

First I draw the diagram. I place one charge at x=-0.80m and the second at x=0.80m. The point at which I want to calculate the potential energy is at (0,0.60m). I apply the Theorem of Pythagoras to get the radial distance from where the point charge is located to the point I want to find potential.

r=Sqrt(x^2 +y^2)
r=1m

Since I have two charges, the Total potential is equal to the sum of both of the charges.
Vtotal= V1 +V2.
Since Both charges are equal and are the same distance apart to the point p,
Vtotal=53940 V.

This is my answer for part A.

for part B, I want to find the potential difference Vb-Va. A charge comes into point P from infinity, So we say that at infinity it has zero potential. However, at P, the potential is -44950 V.

Now, my problem is. Can I use my result from part a to answer part b. Meaning Va=53940 V.
Since the charges are not moving from P (the ones that moved from the x-axis).

Would my answer be Vb-Va=-44950-53940
Vb-Va=-98,890?

Sorry for this beginner problem. I am not sure if I am understanding the concept of Potential due to Point Charges.

 

[gneill]

Part (a) looks good. You might want to express the result to the same number of significant figures as the given data.

For part (b) you need to know the difference between electric potential (Volts) and electric potential energy (Joules). Electric potential energy is associated with the work that needs to be done to assemble a system, bringing in the pieces from infinity where the potential is zero.

You can use the result of part (a) in that the potential energy of a an object with charge q brought to a location where the electric potential is V is given by qV. It's helpful to remember that the Volt is a unit that is made up of other units (a compound unit) namely Volt = Joules/Coulomb, or energy per charge quantity.