Method of images and charges

In summary, the problem involves two conducting planes at a 60 degree angle, with a point charge q placed at a distance a/2 from each plane on the line bisecting the angle. The solution involves finding the coordinates of the image charges to neutralize the potential at the origin, which will result in a total of 6 charges.
  • #1
stunner5000pt
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Homework Statement


To conducting planes are placed at an angle 60 degrees to each other. A point charge q is placed on the line bisecting this angle at a distance a/2 fro each plane. Find the image charges and the resulting potnetial

Homework Equations


[tex] V(0,0) = 0 [/tex]
[tex] V(x,0) = 0 [/tex]
[tex] V(x,2y/\sqrt{3}) = 0 [/tex]

The Attempt at a Solution


Since our charge is located at (a,a) the image charge to make the bottom plane grounded is loacted at a point (a,-a)

Now for hte plane at 60 degrees. the image charge has to be located a distance a/2 from the plate but at an angle. Finding the coordiantes of this point is what is troubling me.

Is it safe to assume that this point is going to be on the Y axis?? such that it turns into the placement like in the diagram??

i hope that is right... so far.

i think to neutralize the potnetial at the origin I am goig to need three more charge located diametrically opoosite location. So in the end we will have 6 charges?? I am currently working on it.

thanks for your help!
 

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  • #2
Since our charge is located at (a,a) the image charge to make the bottom plane
arounded is loacted at a point (a,-a)
WRONG... the charge is located at (a/2, sqrt(3)/2) as in the figure... and the image charge
is (a/2, sqrt(3)/2)...

Now for hte plane at 60 degrees. the image charge has to be located a distance a/2 from the plate but at an angle.
Yup.. you are correct...

Is it safe to assume that this point is going to be on the Y axis?? such that it turns into the placement like in the diagram??
WRONG... the image charge is not on the Y axis...

Finding the coordiantes of this point is what is troubling me.
Then hard work on it... :biggrin:

i think to neutralize the potnetial at the origin I am goig to need three more charge located diametrically opoosite location. So in the end we will have 6 charges?? I am currently working on it.
Yes, you will end up with 6 charges (including the original one)...

GOOD LUCK
 

1. What is the method of images and charges?

The method of images and charges is a technique used in electrostatics and electromagnetism to solve problems involving conductors and charges. It involves creating a mirror image of a charge or a conductor to simulate the effects of other charges or conductors on the original system.

2. How does the method of images and charges work?

The method of images and charges works by using the principle of superposition, which states that the total electric field at a point is the sum of the individual electric fields from each charge or conductor. By creating a mirror image, the electric field from the original system is cancelled out, leaving only the electric field from the image charge or conductor.

3. What are some applications of the method of images and charges?

The method of images and charges has various applications in physics, engineering, and other fields. It is commonly used to calculate the electric field and potential around conductors, such as capacitors and conducting spheres. It is also used in the design of antennas, microwave circuits, and other electronic devices.

4. Are there any limitations to the method of images and charges?

Yes, there are some limitations to the method of images and charges. It only works for problems with simple boundary conditions, such as conductors with sharp edges or point charges. It also assumes that the medium between the charges or conductors is a perfect insulator, which may not always be the case.

5. How do I apply the method of images and charges in problem-solving?

To apply the method of images and charges in problem-solving, you need to first identify the problem as one that can be solved using this method. Then, you need to determine the appropriate image charge or conductor and its location using symmetry and the boundary conditions. Finally, you can use the superposition principle to calculate the total electric field or potential at any point in the system.

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