Image Charges: Two (semi)infinite grounded conducting plates meet at an angle of

Question

Image Charges: Two (semi)infinite grounded conducting plates meet at an angle of 90 degree at the origin. A point charge q is a distance r_0 from the origin along their angular bisector. What image charges are needed to satisfy the boundary conditions and model these grounded plates as a collection of point charges? Specify location, magnitude, and sign. Use multipole expansion to determine the dominant r dependence of the potential along the angular bisector, for r >> r_0. What image charges would be needed to satisfy the boundary conditions and model these grounded plates as a collection of point charges if the angle between the conducting plates was 60 degree? Specify location, magnitude, and sign. Use multipole expansion to determine the dominant r dependence of the potential along the angular bisector for this 60 degree configuration (r >> r_0).

Explanation / Answer

To begin with, assume the semi-infinite grounded plates to be extended to infinity. Now the plates will divide the space into 4 quadrants. The given charge is positive lies on the angle bisector at a distance r0, to solve this problem 3 charges will have to be introduced, 2 negative and 1 positive. The first negative charge will be in the quadrant to the left of the given positive charge at a distance of r0 on the respective quadrants angle bisector. The second positive charge will be a distance 2r0 from the original positive charge in the diagonal quadrant on the anglbisectoror again. The final negative charge will be placed in the remaining quadrant similarly.

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