Electric Potential/Energy question

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In summary, the work required to bring three electrons from a great distance apart to within 1.0 x 10^-10 m from each other depends on the specific configuration of the electrons. However, if they are arranged in an equilateral triangle with each edge being 1 angstrom in length, the total work done would be 3.4 x 10^-18 J.
  • #1
Flaming Toilet
Here's the question: "How much work must be done to bring three electrons from a great distance apart to within 1.0 x 10^-10 m from each other?"

Here's what I did :

.(work to bring one to another)

Work = PE + KE
= PE + 0
=q(V final - V initial) ; V initial = 0
=qV final
=q(KQ/r)
= (1.6 x 10^-19)((9 x 10^9 x 1.6 x 10^-19)/(1.0 x 10^-10))
= 2.3 x 10^-18 J

.(work to bring the other one)

Work = q(KQ/r)
= (1.6 x 10^-19)((9 x 10^9 x 1.6 x 10^-19)/(2 x 1.0 x 10^-10))
= 1.2 x 10^-18 J

. I then add them together to get the total work done

(2.3 x 10^-18 J) + (1.2 x 10^-18 J)
= 3.4 x 10^-18 J

Now, is that right? Feel free to correct me.
 
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  • #2
"How much work must be done to bring three electrons from a great distance apart to within 1.0 x 10^-10 m from each other?"

I may be interpreting the question differently from you. I interpret it to mean that the three electrons are brought into the configuration of an equilateral triangle, with each edge of the triangle r=1 angstrom in length.

If so, then you can compute the final potential energy of one of the pairs of charges with ke2/r, and the final total potential energy of the three charges is three times that (energy from three pairs of charges).
 
  • #3
I see. I'm visualizing the question as three electrons coming together in a line. Bleh, the book didn't provide a diagram. However, I think you're right. Thanks for guiding me in the right direction.
 

1. What is electric potential/energy?

Electric potential/energy refers to the amount of work required to move a unit of electric charge from one point to another in an electric field. It is often measured in units of volts (V) or joules (J).

2. How is electric potential/energy different from electric field?

Electric potential/energy is a measure of the potential energy of a charged particle in an electric field, while electric field is a measure of the force exerted on a charged particle in an electric field. Electric potential/energy is dependent on the position of the particle, while electric field is dependent on the strength and direction of the electric field.

3. How is electric potential/energy related to work?

Electric potential/energy is directly related to work. Work is defined as the force applied over a distance, and in the case of electric potential/energy, the force is an electric force and the distance is the distance moved in the electric field. Therefore, work is required to change the electric potential/energy of a charged particle in an electric field.

4. Can electric potential/energy be negative?

Yes, electric potential/energy can be negative. This occurs when the electric field is directed in the opposite direction of the motion of the charged particle. In this case, work is required to move the particle in the direction of the electric field, resulting in a decrease in electric potential/energy.

5. How is electric potential/energy used in practical applications?

Electric potential/energy is used in a variety of practical applications, including electric circuits, batteries, and electronic devices. It is also used in the study of electrical properties of materials and in the design of electrical systems and equipment.

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