Two charges, Electrical Potential

In summary, with V=0 at infinity, the potential at point C is 9.0μC. Bringing a third charge from infinity decreases the potential by 1.86E2 J.
  • #1

rlc

128
1

Homework Statement


upload_2015-1-22_13-57-41.png

Two charges q = 9.0μ C are fixed in space a distance d = 1.5 cm apart, as shown in the figure.

a) With V = 0 at infinity, what is the electric potential at point C?
b) You bring a third charge q = 9.0μC from infinity to C. How much work must you do?
c) What is the potential energy U of the three-charge configuration when the third charge is in place?

Homework Equations


electrical potential=kq/r
μ=E-6
q=9E9

The Attempt at a Solution


I thought that I should find the distance between q and C using the pythagorean theorem.
((9E9)(9.0E-6)/(2.1213 cm))+((9E9)(9.0E-6)/(2.1213 cm))=7.64E4 V
But this didn't work. The online homework said it was wrong.
Is that the right equation to use? How does the V=0 at infinity affect this problem?
 
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  • #2
What's the SI unit for distance?
 
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  • #3
meters
Was I right to calculate the distance from q to C? Is converting cm to m the only mistake?
 
  • #4
rlc said:
meters
Was I right to calculate the distance from q to C? Is converting cm to m the only mistake?
Yes. Yes No - See post below.
 
Last edited:
  • #5
Note that the legs of the triangle are d/2, not d.
 
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  • #6
Wow, I really need to learn to read these diagrams!
That worked, thank you!

Part b asks: You bring a third charge q = 9.0μC from infinity to C. How much work must you do?
How do I start with this problem?
 
  • #7
Work is closely related to energy.
 
  • #8
The work done by the electric field in moving an electric charge from infinity to point r is
given by:
W= - deltaU= - q(deltaV)= - q(Vr-Vinfinity)= - qVr

I found this equation online. Does it look like the right one to try?
 
  • #9
That's close. One of the annoying things about this topic is that when you calculate work, you have to be clear whether you're talking about the work done by the person moving the charge or the work done by the electric force. The force exerted by the person counteracts the electric force, so the work done by the person has opposite sign of the work done by the electric force. So, you need to consider whether the formula you are using is for the work done by the electric force or for the work done by the person.
 
  • #10
I'm hoping its work done by electric force :)
 
  • #11
rlc said:
I'm hoping its work done by electric force :)
Yes, the formula you wrote is for the work done by the electric force. So, you have to modify it to get the work that you do in moving the charge to C.
 
  • #12
Alright, so I figured it out!
Work=qV
where V is the number I just calculated for the first part of this question and q is the 3rd charge given
So, Work=(9.0E-6)(1.53E7V)=1.37E2 J

Then for part c, it's asking for the potential energy of the three charge configuration when the 3rd charge is in place, which the equation for is:
(work done)+(kq^2)/d
(1.37E2 J) + (9E9)(9.0E-6)^2/(0.015 m) = 1.86E2 J

Thank you for helping me thru this and finding my mistakes! I really appreciate it!
 
1.

What are two charges in electrical potential?

Two charges in electrical potential refer to two objects with opposite charges that interact with each other through an electric field. These charges can be positive or negative and are measured in Coulombs (C).

2.

How is the electrical potential of a charge calculated?

The electrical potential of a charge is calculated by dividing the electrical potential energy by the charge. This is represented by the equation V = U/Q, where V is the potential, U is the potential energy, and Q is the charge.

3.

What is the difference between electrical potential and electric potential energy?

Electrical potential is a measure of the electric potential energy per unit charge at a specific point in an electric field. Electric potential energy, on the other hand, is the energy that a charged object possesses due to its position in an electric field.

4.

How does distance affect the electrical potential between two charges?

According to Coulomb's Law, the electrical potential between two charges is inversely proportional to the distance between them. This means that as the distance increases, the electrical potential decreases and vice versa.

5.

What is the unit of measurement for electrical potential?

The unit of measurement for electrical potential is the Volt (V). It is a derived unit that represents the amount of potential energy per unit charge.

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