Confusion with Electric Potential/Potential Energy

[sisigsarap]

There is a problem I am finding quite confusing:

Two particles, with charges of 20.0 nC and -20.0nC, are placed at the points with coordinates (0,4.00cm) and (0,-4.00cm). A particle with charge 10.0 nC is lcoated at the origin. Find the electric potential energy of the configuration of the three fixed charges.

I am having difficulty understanding the last sentence. For electric potential energy I thought I would use V = 8.99*10^9(q/r) , where I would sum up each charge? For example:

V1 = 8.99*10^9(20nC/4cm) V2 = 8.99*10^9(-20nC/4cm) V3=8.99*10^9(10/0)

Then the Electric potential energy would be V1 + V2 + V3 = 0?

Or would I use U = 8.99*10^9(q1*q2)/(distance from q1 to q2)

and follow the same procedure?

I am very confused with the question and what the book refers to as potential energy and electrical potential??

Any help is appreciated!

Thanks!

 

[Andrew Mason]

Two particles, with charges of 20.0 nC and -20.0nC, are placed at the points with coordinates (0,4.00cm) and (0,-4.00cm). A particle with charge 10.0 nC is lcoated at the origin. Find the electric potential energy of the configuration of the three fixed charges.

Since the electric potential, V, is the potential energy per unit charge it is a scalar quantity that is a function of the separation and the charge. Since it is directionless, potentials can just be added together.

V = U/q = \int_\infty ^R \frac{kQ}{r^2}dr = \frac{kQ}{R} - 0

U = Vq = \frac{kQq}{R}

In order to find the total potential energy, take the potential energy of each pair of charges and add them up (be careful with the signs).

The answer, I think, is -4.5e-5 J.

AM

 

[wais]

The confusion you are experiencing is understandable as electric potential and potential energy are closely related concepts. Electric potential is a measure of the electric potential energy per unit charge at a specific point in space. In other words, it is the amount of electric potential energy that would be experienced by a unit charge if placed at that point.

In this problem, you are asked to find the electric potential energy of the configuration of three fixed charges. This means you need to find the total amount of energy required to assemble the three charges in this specific arrangement.

To do this, you can use the equation U = k(q1*q2)/r, where k is the Coulomb's constant (8.99*10^9 Nm^2/C^2), q1 and q2 are the charges of the two particles and r is the distance between them. You would need to calculate the potential energy for each pair of charges (q1 and q2, q1 and q3, q2 and q3) and then add them together to get the total potential energy of the system.

Alternatively, you can also use the equation V = k(q/r), where V is the electric potential, k is the Coulomb's constant, q is the charge and r is the distance. In this case, you would need to calculate the electric potential at each point where a charge is located and then add them together to get the total potential energy of the system.

In summary, electric potential and potential energy are related but not the same. Electric potential is a measure of potential energy per unit charge, while potential energy is the total amount of energy required to assemble a system of charges in a specific arrangement. I hope this helps clarify your confusion.