[tex]\sf \red{ Question }[/tex]
A thin circular wire ring of radius r carries a charge q. Find the magnitude of electric field strength on the axis of the ring as a function of distance / from its centre. Investigate the obtained function at I>>>r. Find the maximum magnitude of field strength and the corresponding distance I. Also draw the approximate plot of the function E(I).
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Answer:
Electric field due to uniform charged ring on the axis :
Let,
• P = point under consideration
• r = radius of the ring
• dq = point charge
• l = Distance on P (on axis) from the centre of the ring
• R = distance between point charge 'dq' and Point under consideration 'P'
Electric field at point 'P' due to point charge 'dq':
By Pythagoras theorem :
So,
• Total electric field at point P :
• Electric Field in x direction :
Electric field in y direction will be 0 because every element on the ring there is opposite element due to which perpendicular component of the electric field will cancel out each other.
• If l >>> r then,
Therefore, net electric field will be :
• Value of 'l' such that Electric Field is maximum:
I've skipped the basic calculation as the word limit is extended. It's easy you can do it by yourself.