Point Charges in a Square: Could the Force on Each Be Zero?

In summary, the problem involves four charges placed at the corners of a square, with two opposite charges fixed and the other two charges varying. The formula for the force between two charges is given and used to find the relationship between the two fixed charges, resulting in Q = -2q*sqrt(2). The question is then posed if there exists a value for q that would make the resultant force on all four charges zero. After some discussion and calculations, it is concluded that there cannot be a value for q that would satisfy this condition.
  • #1
DietRichCola
6
0

Homework Statement


A charge Q is fixed at each of two opposite corners of a square, while a charge q is fixed at the other two corners. (a) if the resultant electrical force on Q is zero, how are Q and q related? (b) could q be choosen to make the resultant electrical force on every charge zero? explain.
F1 = force between Q's
F2 = force between one Q and q's
a = side of the square


Homework Equations


F = (1/(4*pi*E))(q1*q2/r^2)


The Attempt at a Solution



(a) F1 = (1/(4*pi*E))(Q^2/2a^2)
F2 = (1/(4*pi*E))((Qq*sqrt(2))/(a^2))
I set them equal to each other and got: Q = -2q*sqrt(2)
The answers weren't in the back of the book, so I'm not sure if that's correct or not

The part I'm having trouble with is part (b). I don't think there can be a value for q that would make the forces on all the charges zero, but I don't know how to explain that.

Thanks!
 
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  • #2
whats the distance between the Q's?

and where did the sqr(2) come from in your F2 equation?
 
  • #3
the distance of the side of the square is a, so the diagonal is a*sqrt(2)
 
  • #4
I misread it as (2a)^2.

still don't understand the F2 equation.

you can't just set them equal to each other. they are vectors.
 
  • #5
i saw the equation: (1/(4*pi*E))((Qq)/(a^2)) as the force on one of the sides of the square between Q and q. and i know there's another force pointing perpendicular on the adjacent side of the square. the addition of those two vectors would give me the hypotenuse of a 45-45-90 triangle. therefore, i saw that the magnitude of the hypotenuse is that force times sqrt(2).
would that be right?
 
  • #6
sounds good.
 
  • #7
that's good.
do you know about part (b) ?
 
  • #8
you know what q must be for the force on Q to be zero. what must the charge on Q be to make the force on q be zero?
 
Last edited:
  • #9
Since it's a square, the charge for q would be the same formula as it was for Q, just the Q and q are switched:
q = -2Qsqrt(2)
 
  • #10
yes. and so? what is your conclusion?
 
  • #11
so would that mean that the value of q would be -Q ?
i know q =/= Q because then the charges would all repel each other.
if i plug one equation into the other, like: q = -2(-2q*sqrt(2))sqrt(2), i just get that q=8q. which is why i think there can't be a value for q. though, i don't know the explanation.
 

1. What is a point charge?

A point charge is a hypothetical particle with a specific amount of electrical charge concentrated at a single point in space. It is often used in physics and engineering as a simplified model for understanding the behavior of electric fields and forces.

2. How is the force on each point charge in a square determined?

The force on each point charge in a square is determined by the electric field at the location of the charge and the amount of charge it possesses. The electric field is a vector quantity that represents the strength and direction of the force experienced by a charged particle in that location. Summing up the forces on each point charge will give the net force on the entire system.

3. Can the force on each point charge in a square be zero?

Yes, it is possible for the net force on each point charge in a square to be zero. This can happen if the charges are arranged in a specific way such that the electric fields created by each charge cancel each other out. This is known as an electrically neutral configuration.

4. What factors affect the force on each point charge in a square?

The force on each point charge in a square is affected by the magnitude and sign of the charge, the distance between the charges, and the direction of the electric field. The force is also influenced by the presence of other charges in the surrounding environment.

5. Why is it important to understand the force on each point charge in a square?

Understanding the force on each point charge in a square is important in many areas of science and engineering. It can help us analyze and predict the behavior of electric fields and forces, which are fundamental in many natural and technological processes. This understanding is also essential for designing and optimizing circuits, electronics, and other devices that rely on electric fields and forces.

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