How do I draw the diagram of the mirror charge

In summary, the problem involves two point charges (+q and -q) placed at specific positions in a cartesian reference frame. The half space of positive x is occupied by a conductor. The task is to determine the positions and values of the mirror charges in this scenario. To visualize this, a sketch can be made on the yz-plane, with the conductor indicated on the +x side and the empty space on the -x side. The interface between the two can be represented as a 'cutaway' section to show that it extends indefinitely.
  • #1
blueyellow

Homework Statement



Two point charges +q and -q are placed respectively in positions (-a, 0, +a) and (-a, 0, -a) of a cartesian reference frame, with a being positive and known. The half space of positive x is fully occupied by a conductor. What are the positions and values of the mirror charges in this specific case?

The mirror charge for +q is: -q at (a, 0, +a)
The mirror charge for -q is: +q at (a, 0, -a)

DRAW A SKETCH
how do I do this considering that 'the half-space of positive x is fully occupied by a conductor'

The Attempt at a Solution



drawing a line at y=0, z=0 on the x-axis but only for positive x
but this is wrong
 
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  • #2
What geometrical object describes the interface between the filled half-space and the unfilled half space?
 
  • #3
all i could picture was this semi-infinite block filling the positive x space. but since you said the word 'interface' does it mean i can just sort of not see it as a block, and just see it as an infinite plane on the y-z plane? so i sketch the y-z plane?
 
  • #4
Everything is at y = 0, so I suggest you draw/sketch the zx-plane .
 
  • #5
"The half space of positive x is fully occupied by a conductor"
i can't understand this line?
which space?
 
  • #6
blueyellow said:
all i could picture was this semi-infinite block filling the positive x space. but since you said the word 'interface' does it mean i can just sort of not see it as a block, and just see it as an infinite plane on the y-z plane? so i sketch the y-z plane?

You can sketch the yz plane and indicate that to the +x side is conductor, and to the -x side is empty space. If you want to get fancy, you can indicate a portion of the conductor region as a 'cutaway' section, implying that it extends indefinitely. Something like this:

https://www.physicsforums.com/attachment.php?attachmentid=37208&stc=1&d=1310746184
 

Attachments

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1. How do I determine the position of the mirror charge in the diagram?

The position of the mirror charge is always located at the same distance behind the mirror as the original charge is in front of the mirror. This distance is known as the object distance, and it can be measured from the vertex of the mirror to the original charge.

2. What is the direction of the mirror charge in the diagram?

The direction of the mirror charge is always opposite to the direction of the original charge. This is because the mirror charge is a reflection of the original charge and will have an equal but opposite charge from the original charge.

3. How do I determine the magnitude of the mirror charge?

The magnitude of the mirror charge is equal to the magnitude of the original charge. This is because the mirror charge is a reflection of the original charge and will have the same magnitude but opposite sign.

4. What is the purpose of drawing the mirror charge in the diagram?

The mirror charge is drawn in the diagram to show the electric field lines that would be produced by the original charge in the presence of the mirror. This allows us to visualize the electric field and understand how it is affected by reflections and mirror charges.

5. Can I use the mirror charge diagram to calculate the electric field at a specific point?

Yes, the mirror charge diagram can be used to calculate the electric field at a specific point. By using the principle of superposition, we can add the electric field vectors from the original charge and the mirror charge to determine the electric field at any point in between.

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