Force on (+q) in a Square Configuration

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In summary, the question involves calculating the magnitude of the force on a charge arranged in a square with 4 other charges. The x and y components of the force are equal by symmetry and therefore the magnitude can be calculated using the formula F = \sqrt{2} K q \frac{Q}{L^2}. However, the textbook provides a different answer, F = (2 - \sqrt{2}) K q \frac{Q}{L^2}, which may be due to a missed step in computing the projection in the x direction.
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awvvu
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Homework Statement


4 charges are arranged in the corners of a square of lengths L as follows:

(-Q) --------- (+q)
|
|
|
(+4Q) ------- (-Q)

What is the magnitude of the force on the (+q)?

The Attempt at a Solution


My answer doesn't match up with my book's.

x-component of the force is, where K is [itex]\frac{1}{4 \pi \epsilon_0}[/itex]:

[tex]F_x = K q(\frac{- Q}{L^2} + \frac{4Q}{2 L^2}) = K q \frac{Q}{L^2}[/tex]

The x and y components of the force are equal by symmetry:

[tex]\vec{F} = K q \frac{Q}{L^2} (\hat{x} + \hat{y})[/tex]

Therefore the magnitude is:

[tex]F = \sqrt{2} K q \frac{Q}{L^2}[/tex]

However, my textbook says the answer is:

[tex]F = (2 - \sqrt{2}) K q \frac{Q}{L^2}[/tex]

I have no idea where they got the "2" term from. I probably just made a careless mistake somewhere, but I can't see it.
 
Last edited:
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  • #2
Bump -- anyone?
 
  • #3
so, in F_x,when computing F(4Q)

you must 1 compute L, and then compute projection in x, i guess that wasn't made...
i made [tex]Kq \frac{4Q}{\frac{L}{cos(45º)}^{2}}*cos(45º)[/tex]

gretts
littlepig

P.s, Sorry, but i give up, 10m to try making the equation and i still couldn't do it...
 
Last edited:
  • #4
Ah, that's exactly it! I always forget to do that. Thanks.
 

What is Simple Coulomb's Law?

Simple Coulomb's Law is a fundamental law in physics that describes the electrostatic interaction between two charged particles. It states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

What is the equation for Simple Coulomb's Law?

The equation for Simple Coulomb's Law is F = k * (q1 * q2) / r^2, where F is the force, k is the Coulomb's constant, q1 and q2 are the charges of the two particles, and r is the distance between them.

What is the unit of measurement for Simple Coulomb's Law?

The unit of measurement for Simple Coulomb's Law is Newtons (N), which is a unit of force in the International System of Units (SI).

How do you calculate the force between two charged particles using Simple Coulomb's Law?

To calculate the force between two charged particles, you need to plug in the values of the charges and the distance between them into the Simple Coulomb's Law equation. Make sure to use consistent units and use the appropriate value for the Coulomb's constant based on the units used.

What are some real-life applications of Simple Coulomb's Law?

Simple Coulomb's Law has many practical applications, including determining the force between charged particles in an atom, calculating the force between two charged particles in an electrical circuit, and understanding the behavior of charged particles in electric and magnetic fields. It is also used in various fields such as electronics, telecommunications, and medical imaging.

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