- #71
TSny
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PeroK said:What if you consider a small element on the right, and calculate the tension on that and take the limit as the size of the element goes to zero?
I don't know if that would work out. It's just an idea.
etotheipi said:Actually that's a pretty good idea, have some (no longer infinitesimal) control region on the right that subtends an angle ##\alpha## or something, and try to come up for an expression for the electrostatic force on that.
It's slightly more complicated maths-wise and I'm not so sure how best to do it yet, but I think that would give something useful! Let me think about it for a while
Thanks!
This a good approach. For an infinitesimal segment subtending angle ##\alpha##, the force on the segment is due to the net electric field of all of the charge of the ring excluding the charge in the segment itself. (The field due to the segment does not exert a net force on the segment itself.) So you just need to modify the limits of the integral ##I## in the OP. Everything else in that post looks good. When I carry out this procedure, I get an expression for ##T## that agrees with ##T = F/2## in post #39 in the limit of infinitesimally small ##\alpha##. In particular, you get the logarithmic divergence as ##\alpha## approaches zero.