Electrical Potential Energy

In summary, the problem involves two point charges, Q1 = 3.3 µC and Q2 = 7.6 µC, initially very far apart, which are brought together with a final separation of 2.6 m. The work required to bring them together is calculated using the equation Work = -\DeltaPE, where k is the Coulomb constant, Q1 and Q2 are the charges, and r is the separation distance. The final potential energy is found to be 0.0868 J and the initial potential energy is negligible. Therefore, the work done to bring the charges together is 0.0868 J. There may be some confusion regarding the sign of the work, as different sources may
  • #1

Homework Statement



Two point charges Q1 = 3.3 µC and Q2 = 7.6 µC are initially very far apart. They are then brought together, with a final separation of 2.6 m. How much work does it take to bring them together?

Homework Equations



[tex]\Delta[/tex]PE = ( k Q1 Q2 ) / r

Work = - [tex]\Delta[/tex]PE

k= 8.99 e 9

The Attempt at a Solution



PE final = k Q1 Q2 / r
= (8.99e9)(3.3e-6)(7.6e-6) / ( 2.6m)
= 0.0868 J

PE initial = k Q1 Q2 / r
with r initial being infinitely large PE initial is basically 0

so [tex]\Delta[/tex]PE = 0.0868 + 0
Work = - [tex]\Delta[/tex]PE = -0.0868What is the error in this? Thank you!
 
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  • #2
Is the separation 2.6 m or 2.8 m? And do not forget the unit of work!ehild
 
  • #3
It was 2.6m...I fixed it. I found that the answer was just 0.0868 not -0.0868. My teacher said the equation was Work = -[tex]\Delta[/tex]PE, but I found it some place else that shows it as just Work = [tex]\Delta[/tex]PE. Which is correct?
 
  • #4
The work needed to bring the charges together was the question. It is some external force Fe (maybe your force) that does this work. The external force is opposite and at least equal in magnitude with the Coulomb force Fe=-Fc. As the charges repel each other, the external force must push them toward the centre, so the direction of the external force is the same as the displacement: the work is positive.

ehild
 
  • #5


There is no error in this solution. You have correctly used the formula for electrical potential energy and calculated the work required to bring the two point charges together. However, it should be noted that this is the work done by the external force in bringing the charges together, and not the total work done, as there may also be work done by the electric field of the charges themselves. Additionally, it is important to include the units in your final answer, so the correct answer would be -0.0868 J.
 

1. What is electrical potential energy?

Electrical potential energy is the energy that an object possesses due to its position in an electric field. It is a form of potential energy that is associated with the interaction between electric charges.

2. How is electrical potential energy different from electrical potential?

Electrical potential energy is the energy that a charged object has due to its position in an electric field, while electrical potential is the amount of potential energy per unit charge at a specific point in an electric field. In other words, electrical potential energy is the potential energy of a single charged object, while electrical potential is the potential energy per unit charge at a specific point in an electric field.

3. What factors affect the amount of electrical potential energy?

The amount of electrical potential energy depends on the charge of the object, the distance between the charged object and the point in the electric field, and the strength of the electric field. The greater the charge and the closer the object is to the point in the electric field, the higher the electrical potential energy will be.

4. Can electrical potential energy be converted into other forms of energy?

Yes, electrical potential energy can be converted into other forms of energy, such as kinetic energy. When a charged object moves in an electric field, it can convert its electrical potential energy into kinetic energy.

5. How is electrical potential energy measured?

Electrical potential energy is measured in joules (J) in the SI system of units. It can also be measured in electron volts (eV) or kilowatt-hours (kWh) in other systems of units.

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