1. suppose you have a charged conducting sphere with a hollow center and a hole in its side leading to the center, like the metal piece at the top of a van de Graaf generator. The electric field strength at the surface decreases to zero as the surface is followed to the interior of the hollow.
Does it take the same amount of work to move a test charge from a great distance away to a point on the surface at the center of the hollow as to move the charge to a point on the outer surface?
2. similar to #1 except this time you have a charged conducting sphere with a conducting needle with a sharp tip sticking out from its side. The electric field strength becomes very intense near the pointed tip of the needle.
Same question as #1 - does it take the same amount of work to move a test charge from a great distance away to the tip of the needle as to move the charge to the smoothly rounded surface?
In both cases, I think the answer is yes, but what physics principle answers the questions?
I'm assuming that even though the field lines are visualized as closer together near the needle tip and further apart (to the point of not existing) near the hollow inside, each line is equivalent to any other line in terms of the work that must be done in moving a test charge from a great distance away, along each line to the surface of the object. Does that sound correct?
Does it take the same amount of work to move a test charge from a great distance away to a point on the surface at the center of the hollow as to move the charge to a point on the outer surface?
2. similar to #1 except this time you have a charged conducting sphere with a conducting needle with a sharp tip sticking out from its side. The electric field strength becomes very intense near the pointed tip of the needle.
Same question as #1 - does it take the same amount of work to move a test charge from a great distance away to the tip of the needle as to move the charge to the smoothly rounded surface?
In both cases, I think the answer is yes, but what physics principle answers the questions?
I'm assuming that even though the field lines are visualized as closer together near the needle tip and further apart (to the point of not existing) near the hollow inside, each line is equivalent to any other line in terms of the work that must be done in moving a test charge from a great distance away, along each line to the surface of the object. Does that sound correct?