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Homework Statement
I need help on solving this exercise :
We have a ring of radius = ##a## uniformly charged (total charge = ##Q##) and on its axis a segment ##OA## (length = ##a## also) of uniformly distributed positive electric charges with the charge density ##\lambda'## and of total charge = ##Q## (the same as the ring).
I'm asked to determine the total force ##\vec{F}## that the ring's distribution is exerting on the segment's distribution.
Homework Equations
##\vec{F}=q.\vec{E}##
The Attempt at a Solution
First of all we have, for a point ##M## of ##OA## :
##\vec{F}_{Ring/M}=k\frac{Q.\lambda'dz}{a^2+z^2}\vec{u_z}## with ##k\frac{Q}{a^2+z^2}\vec{u_z}=## the electric field created at ##M##.
##\Rightarrow \vec{F}_{Ring/OA} = kQ\lambda'\int_0^a \frac{dz}{a^2+z^2}\vec{u_z} = kQ\lambda'\frac{\pi}{4a}\vec{u_z}##
Where have I gone wrong?
Thank you!
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