Calculating Coulomb Force on a Point Charge in a Square Distribution

In summary, the conversation discusses finding the force on a point of charge of 30μC at (0,0,5)m due to a 4m square on the z=0 plane between x=±2m and y=±2m with a total of 500μC, distributed uniformly. The conversation also includes a discussion of using double integrals and calculating the z-component of the force. The final result is 4 N, which differs from the answer provided in the text of 4.66 N.
  • #1
azizlwl
1,066
10

Homework Statement


Find the force on a point of charge of 30μC at (0,0,5)m due to a 4m square int he z=0 plane between x=±2m and y=±2m with a total of 500μC, distributed uniformly.

Homework Equations

The Attempt at a Solution


R=-x,-y,+5z
dQ=ρdydx=500/4 dydx

dE=dQ(5az) / (4πε0((x2+y2+25)3/2 )
x and y-axis cancel

How to do integral with x2 and y2 in the denominator?

Ans. 4.66azN
 
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  • #2
... use the relationship of dQ to dx and dy to make a double integral.
 
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  • #3
Simon Bridge said:
... use the relationship of dQ to dx and dy to make a double integral.
Simon Bridge said:
... use the relationship of dQ to dx and dy to make a double integral.
 
  • #4
Actually I really don't understand the question. Area enclosed by x=±2 and y=±2 will be 16m square. What does it means by" due to a 4m square "?
 
  • #5
azizlwl said:
Actually I really don't understand the question. Area enclosed by x=±2 and y=±2 will be 16m square. What does it means by" due to a 4m square "?
Draw a square 4 m per side. Distribute 500 μC uniformly on the edges (so each side of the square is a line segment with 500/4 μC on it.
 
  • #6
F1d=3x5x9/16 ∫-22 dy (√29d -yay)/(29+y2)3/2
F1d=8.43 x 0.129 =1.087
The integral value using app integral calculator.
F1z=1.087 x 5 /√29 = 1.009.

Total force= 4Naz less than the answer..
 
  • #7
azizlwl said:
F1d=3x5x9/16 ∫-22 dy (√29d -yay)/(29+y2)3/2
F1d=8.43 x 0.129 =1.087
The integral value using app integral calculator.
F1z=1.087 x 5 /√29 = 1.009.

Total force= 4Naz less than the answer..
I don't understand what your last line is trying to convey. Can you explain in more detail?
 
  • #8
4 segments, so I added all that z-axis component. X and y-axis cancelled. The answer is 4.66azN
 
  • #9
So your result is about 4 N and the answer given in the text is 4.66 N ?

I'm inclined to agree with your result over that of the book.
 
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What is the definition of Coulomb Forces?

Coulomb Forces, also known as electrostatic forces, are the attractive or repulsive forces between two electrically charged particles. These forces are governed by Coulomb's Law, which states that the magnitude of the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between the particles.

How do Coulomb Forces differ from gravitational forces?

Coulomb Forces and gravitational forces both involve the interaction between two objects, but they differ in terms of the type of force and the properties of the objects involved. While Coulomb Forces are electrical in nature and act between charged particles, gravitational forces are caused by the mass of objects and act between any two objects with mass. Additionally, Coulomb Forces can be both attractive and repulsive, while gravitational forces are always attractive.

What is the SI unit of Coulomb Forces?

The SI unit of Coulomb Forces is newtons (N). This is the standard unit of measurement for all types of forces, including Coulomb Forces.

How do Coulomb Forces affect the behavior of matter?

Coulomb Forces play a crucial role in determining the behavior and properties of matter. They are responsible for holding atoms together to form molecules, as well as determining the strength and stability of chemical bonds. Additionally, Coulomb Forces are essential in the functioning of electrical circuits and the behavior of charged particles in electromagnetic fields.

How can Coulomb Forces be manipulated or controlled?

There are several ways in which Coulomb Forces can be manipulated or controlled. One method is by altering the amount or type of charge on an object, which will affect the strength of the force. Another way is by changing the distance between charged particles, as the force is inversely proportional to the square of the distance. Additionally, external electric fields can be used to influence the behavior of charged particles and their interactions with each other.

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