Electrostatics - force on point charges by electric field

[risk2112]

Homework Statement

A square, with each corner as a point charge, A, B, C, and D. They all have the same charge of 5.0 x 10 ^(-6) C. Length of each side of the square is 0.1 m. 2 negative charges diagonal from each other, and the other two are positive, diagonal from each other.
Question asks net force on each point charges and electric field and electric potential at centre of the square.
A, B, C, D = 5.0 x 10^(-6) C
radius = 0.1 m
2 negative charges diagonal
2 positive charges diagonal
Square of four corners A, B, C, D.

Homework Equations

F_e = kq1q2/r^2
F_e = qE
idk equation for electric potential

The Attempt at a Solution

For each net force, are they all the same except with opposite directions? Like say 5 N NW, 5 SW, 5 SE, 5 NE. If so, then I can figure out that part.
I really have no idea for the electric potential or electric field, but I am guessing one of the two is going to have either an electric potential of 0 or electric field of 0. I don't know how to solve for either of them though.

 

[risk2112]

I calculated the force, being 9.1 x 10^(something, forgot) N, but I don't know how to use F_e for the middle, with a charge in the middle as q...in order to get E (electric field) for middle. Also, is the E for electric field what makes V (electric potential) = radius x electric field?

 

[thomate1]

Yes, the net force on each point charge will be the same in magnitude but with opposite directions. This is because the charges are all the same and equally spaced, so the electric field at the center of the square will be equal and opposite for each charge.

To calculate the electric field at the center of the square, we can use the equation F_e = qE, where F_e is the net force on the charge, q is the charge, and E is the electric field. Since we know the net force and the charge, we can rearrange the equation to solve for the electric field. The electric field at the center of the square will be the same for each charge, since they are all equidistant from the center.

To calculate the electric potential at the center of the square, we can use the equation V = kq/r, where V is the electric potential, k is the Coulomb's constant, q is the charge, and r is the distance from the charge to the center. Since the charges are all the same and equally spaced, the electric potential at the center of the square will be the same for each charge.

Using these equations, we can calculate the net force, electric field, and electric potential at the center of the square for each charge. It is important to note that the electric field and electric potential are vector quantities, so they will have both magnitude and direction. The direction of the electric field will be towards the negative charges and away from the positive charges, while the direction of the electric potential will depend on the location of the charges and the center of the square.

I hope this helps clarify the concepts of electrostatics and how they apply to this specific scenario. Keep exploring and asking questions to deepen your understanding of this fascinating subject!