- #1
*FaerieLight*
- 43
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I've just worked out using the method of images that the total induced charge on a grounded hollow conducting sphere in the presence of a dipole outside the sphere pointing in the radial direction is non-zero. I can't think of an intuitive explanation as to why a dipole outside would induce a non-zero charge on the sphere.
I think the problem goes back to why a point charge outside a hollow conducting sphere would induce a net charge on the sphere that is not equal in magnitude to the point charge, which seems to be the case also, according to the method of images. I suppose there is no reason for the induced charge to be equal to the point charge in magnitude, but then for a grounded conducting plane, with a point charge above it, the induced charge on the plane is the same in magnitude to the point charge! I don't get why it should be equal in magnitude for a plane, and why it isn't for a sphere. I know they have different geometries but I can't see what specific difference in their geometries leads to the difference in induced charge magnitude.
Could someone please help me understand this?
Thanks a lot!
I think the problem goes back to why a point charge outside a hollow conducting sphere would induce a net charge on the sphere that is not equal in magnitude to the point charge, which seems to be the case also, according to the method of images. I suppose there is no reason for the induced charge to be equal to the point charge in magnitude, but then for a grounded conducting plane, with a point charge above it, the induced charge on the plane is the same in magnitude to the point charge! I don't get why it should be equal in magnitude for a plane, and why it isn't for a sphere. I know they have different geometries but I can't see what specific difference in their geometries leads to the difference in induced charge magnitude.
Could someone please help me understand this?
Thanks a lot!