Calculating Force on Charge q near Washer

In summary, the problem asks for the force felt on a charge q located at a distance D from the center of a washer with inner radius a and outer radius b, which has a constant surface charge density σ. To solve this, Gauss's law cannot be used since the problem is not cylindrically symmetric. However, a good approach is to choose a random spot on the washer and determine the separation vector \vec{r} from that spot to the charge q. By integrating over all possible random spots, the total force \vec{F} on q can be found.
  • #1
shannon
11
0

Homework Statement


There is a washer (inner radius is a and outer radius is b) on the x-y axis with a constant surface charge density σ . What is the force felt on charge q on z-axis distance D from center of washer.


Homework Equations





The Attempt at a Solution


I don't even know where to begin...
I was thinking about drawing a triangle to a random spot on the washer from the origin to the charge q...but I don't know if that will work since it's a washer.
I don't think I can pick a gaussian surface...can I?
Please give some hints!
 
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  • #2
Gauss's law is only useful under cylindrically symmetric cases when the cylinder extends to infinity, or it is very long and you are far from the ends; neither of these conditions are met by this problem, so that method is out.

Your idea of drawing a triangle to a random spot on the washer (x,y,0) is good. What is the separation vector [itex]\vec{r}[/itex] from the point (x,y,0) to the point (0,0,D)?How much charge [itex]dq[/itex] is contained in the infinitesimal area [itex]dxdy[/itex]? What does that make [itex]\vec{E}[/itex]? How about [itex]\vec{F}[/itex]?
 
  • #3
Thank you very much for the help!

But I'm still a little puzzled about the problem...If I pick a random spot on the washer, then I won't know the exact distance from the origin, so I can't have a specific value for the separation vector. Right?

So, can I pick a spot on the outer radius b?
 
  • #4
Well, give your random spot the coordinates (x,y,0), what is the separation vector in terms of x and y? Remember, you are going to end up integrating over all possible random spots, so you can't restrict yourself to only those spots that are along the outer radius.
 

1. How do you calculate the force on a charge near a washer?

To calculate the force on a charge near a washer, you will need to use Coulomb's Law which states that the force between two charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them. You will also need to use the formula for the electric field created by a charged washer, which is equal to the charge divided by 2πε0r, where ε0 is the permittivity of free space and r is the distance from the washer to the charge.

2. What is the direction of the force on a charge near a washer?

The direction of the force on a charge near a washer will depend on the polarity of the charge and the direction of the electric field created by the washer. If the charge and the electric field have the same direction, the force will be repulsive, and if they have opposite directions, the force will be attractive.

3. Can the force on a charge near a washer be negative?

Yes, the force on a charge near a washer can be negative. This can happen when the charge and the electric field have opposite directions, resulting in an attractive force. This can also happen if the charge is negative and the electric field is positive, resulting in a negative value for the force.

4. How does the distance from the washer affect the force on a charge?

The distance from the washer has an inverse relationship with the force on a charge. This means that as the distance increases, the force decreases, and as the distance decreases, the force increases. This is because the electric field decreases as the distance increases, according to the formula for the electric field.

5. Can the force on a charge near a washer be zero?

Yes, the force on a charge near a washer can be zero. This can happen when the charge is located at the center of the washer, where the electric field is zero. This can also happen if the charge and the electric field have opposite directions and cancel each other out, resulting in a net force of zero.

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