Superposition of electric forces question

• jessicak
In summary, the net electric force exerted by four point charges of +/-Q arranged on the corners of a square on a point charge q placed at the center of the square is 8kQq/L^2cos(45). The y components of the forces cancel out, leaving 4 equal forces in the positive x direction. The Pythagorean theorem is used to find the distance between charges, and the formula F=kQq/r^2 is used to calculate the magnitude of each force.

Homework Statement

Four point charges of +/-Q are arranged on the corners of a square of side L. What is the net electric force that these charges exert on a point charge q placed on the center of the square (formula in terms of Q, q, L and Coulumb constant k)?

F=kQq/r^2

The Attempt at a Solution

The four electric forces point in two directions, two to the upper right handed corner and two to the lower right hand corner. These forces are all equal in magnitude because they each have the same magnitude of charge. The y components of these forces cancel, because they are in opposite directions. I also used the Pythagorean theorem to find the distance between charges. That leaves 4 forces equal in magnitude in the positive x direction. Solving for one of these charges gives:

F= (kqQ/0.5L2)cos(45)= 2kqQ/L2cos(45)

I'm then thinking to multiply this by 4, but I'm not getting the correct answer. Any help would be appreciated

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ehild

I'm getting 8kQq/L2cos45

I have online hw, so when I submit it it's not correct, but I'm not seeing where I'm going wrong

Evaluate 8 cos45.

ehild

I feel a little silly now, thanks!

:tongue:

1. What is superposition of electric forces?

The superposition of electric forces is a principle in physics that states that the total electric force on a charged particle is equal to the vector sum of the individual electric forces acting on it. In other words, if there are multiple electric forces acting on a particle, the net force is found by adding up all the individual forces.

2. How does superposition of electric forces apply to multiple charges?

When dealing with multiple charged particles, the superposition principle allows us to calculate the total electric force on each particle by considering the individual forces from all the other particles. This is useful in understanding the behavior of electrically charged systems, such as atoms and molecules.

3. Can the superposition of electric forces be applied to non-point charges?

Yes, the superposition principle can be applied to any charged object, even if it is not a point charge. In this case, the forces are calculated by breaking the object into smaller parts and considering the individual forces on each part.

4. How does distance affect the superposition of electric forces?

The superposition of electric forces is inversely proportional to the square of the distance between the charged particles. This means that as the distance between particles increases, the force between them decreases. This is known as Coulomb's law.

5. What other principles are involved in the superposition of electric forces?

The superposition principle is closely related to the principles of conservation of charge and Newton's third law of motion. Conservation of charge states that the total amount of charge in a closed system remains constant, while Newton's third law states that for every action, there is an equal and opposite reaction. Both of these principles play a role in the superposition of electric forces.