Where can I find the image charge for a point charge near conducting surfaces?

[Reshma]

Someone's got to help me on these two.

1)Two semi-infinite grounded conducting planes meet at right angles. In the region between them, a point charge q is kept such that it is at a distance of 40cm from each of the two planes[i.e.(40,40)]. Find the position of its image charge/charges.

2)A point charge q is placed in the vicinity of a conducting sphere. Find the poition of its image charge.

Just in case...An image charge will produce zero potential together with q.

 

[OlderDan]

Someone's got to help me on these two.

1)Two semi-infinite grounded conducting planes meet at right angles. In the region between them, a point charge q is kept such that it is at a distance of 40cm from each of the two planes[i.e.(40,40)]. Find the position of its image charge/charges.

2)A point charge q is placed in the vicinity of a conducting sphere. Find the poition of its image charge.

Just in case...An image charge will produce zero potential together with q.

Have you thought about what the optical image(s) would be if you placed an object in the symmetry plane between two mirrors at right angles? How many images would be formed, and where would they be? For charges, image charges must have the opposite sign to have constant (zero) potential at the surface. When multiples surfaces are involved there can be images of images, just as there are for optical images.

 

[Reshma]

Have you thought about what the optical image(s) would be if you placed an object in the symmetry plane between two mirrors at right angles? How many images would be formed, and where would they be? For charges, image charges must have the opposite sign to have constant (zero) potential at the surface. When multiples surfaces are involved there can be images of images, just as there are for optical images.

Thank you very much! I think this solves my first problem.

Since my charge is located in the 1st quadrant, I should have one image charge in each of the other three quadrants(total=3). So by your explanation my image charges are located at (-40,40), (-40,-40), (40,-40). Is my answer correct?

However in the 2nd problem, I don't know how to exploit the symmetry for the sphere. Can you help me on that?

 

[Reshma]

Can someone help?