Finding the force acting on a point charge with a disk around it

In summary, the conversation is discussing a calculation error in which the answer should be F = -99.4 az μN. The question asks for clarification on what the variable R stands for in the second equation, and the response is that it stands for radius. The following discussion delves into the details of the calculation and clarifies the position and size of the disk. Ultimately, the correct calculation results in an electric field of 3.313269 V/m and a force of 99.39808 µN.
  • #1
falyusuf
35
3
Homework Statement
Attached below.
Relevant Equations
Given below.
Question:
20089301620236335838842342050563270.png

Here's my attempt with the relevant equations:
1637708550496.png

The correct answer is F = -99.4 az μN. Could someone please figure out my mistake?
 
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  • #2
Let's consider the second equation (E=...). What does R stand for?
 
  • #3
Gordianus said:
Let's consider the second equation (E=...). What does R stand for?
Radius.
 
  • #4
Hmmm...Try again
 
  • #5
The position of the disk in space is not clear. What does it mean "a disk located 0<ρ<1 " that is, the center of the disk is in the z axis or is displaced by 1 m and the radius of the circle is 1 m or only 1/2 m. It is not clear at all.
 
  • #6
I think I got how was calculation done. The circle of radius 1m with the center located on z axe. If we consider an infinite small surface dS=r*dα*dr [as in attached sketch] then:
dE=ρs/(4/PI()/εo/a^3*dS*ā
E=ρs/(4/PI()/εo*ʃdS*ā/sqrt(r^2+d^2)/(r^2+d^2)
E=ρs/(4/PI()/εo*ʃdS*ā/(r^2+d^2)^3/2
E=ρs/(4/PI()/εo*ʃʃdr*r*dα*ā(r^2+d^2)^3/2 [one integral for dr and another for α]
The component radial ȓ is cancel out, because of all direction of component radial ȓ around z
E=2*pi()*ρs/4/PI()/εo*ʃdr*r*ž/(r^2+d^2)^3/2 |ž|=d
E=ρs/2/εo*d*ʃdr*r/(r^2+d^2)^3/2
Let’s put x=r^2+d^2 then dx=2*r*dr or r*dr=dx/2 ; r=0 x=1 r=1 x=2
ʃdx/2/x^3/2=1/2/(-3/2+1)*x^(1-3/2)=-1/x^0.5|x=1 to x=2|
-1/sqrt(2)+1/sqrt(1)= 0.292893
E=ρs/2/εo*d*0.292893=3.313269 V/m
F=3.313269*30=99.39808 µN
 

Attachments

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Related to Finding the force acting on a point charge with a disk around it

1. What is the formula for finding the force acting on a point charge with a disk around it?

The formula for finding the force acting on a point charge with a disk around it 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 point charge and the disk, and r is the distance between them.

2. How do you determine the direction of the force on a point charge with a disk around it?

The direction of the force can be determined using the principle of superposition, where the direction of the force is along the line connecting the two charges and away from the charge with the same sign, and towards the charge with the opposite sign.

3. Can the force acting on a point charge with a disk around it be negative?

Yes, the force acting on a point charge with a disk around it can be negative if the two charges have opposite signs, resulting in an attractive force between them.

4. How does the distance between the point charge and the disk affect the force?

The force between the point charge and the disk is inversely proportional to the square of the distance between them. This means that as the distance increases, the force decreases and vice versa.

5. What is the significance of the disk in the force calculation?

The disk plays a crucial role in determining the force acting on the point charge as it is the source of the electric field that exerts the force on the point charge. The size and charge of the disk can greatly impact the magnitude and direction of the force.

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