So I know that the E-field at any point along the central axis of a charged loop is kqz/(r^2 + z^2)^(3/2) where z is the distance along the central axis, but would it be the same if you weren't along the central axis? I was thinking this might be similar to the law that the charge contained within a conductive shell is zero at any position: if you move towards one side, the field from that side becomes stronger but there is more sphere on the other side to counteract it.
Is this analogous to the charged loop?
Is this analogous to the charged loop?
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No, it's not the same. It works inside a sphere because because the field follows an inverse square law, and the area subtended by a solid angle depends on the square of the distance. The two effects cancel.
But with the ring, the length of ring subtended by an angle depends linearly on the distance. The field due to each small bit of ring still follows an inverse square law. The two effects won't cancel.
But with the ring, the length of ring subtended by an angle depends linearly on the distance. The field due to each small bit of ring still follows an inverse square law. The two effects won't cancel.
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You're welcome. I'm glad to help. People don't usually think about why this works for a sphere, so I'm glad you asked.
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