Electric field strength between two rings:

Jul 2018
Hi to everyone! I'm here to ask how could you resolve this problem about electric fields: two charges q1= 1.88*10^-8 and q2=-7.54*10^-8 are evenly distributed on two rings with the same radius R=30 cm, positioned above two parallel planes, far each other d=3mm. We have to calculate the strength that the first ring applies on the second ring (NOT IN THE CENTRE, BUT IN EACH MICRO-PART OF THE RING). Someone suggested me to approximate the rings with two wires because d<<R and that actually works. But I wanna have a formula which is always effective foe the calculus, not only in this case. Someone else suggested me to consider the the variable distance with the polar coordinates: x1=Rcost, y1=Rsint and z1=0 for the first ring and x2=Rcosp, y2=Rsinp and z=d , then find the result of:

K*q1q2* Double Integral from 0 to 2Pi of 1/((R^2(cost-cosp)^2)+(R^2(sint-sinp)^2)+d^2)) But the result of integral is 0 and it does not make sense. SOME CAN HELP ME!!! Thanks very much to everyone!!


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