A cone made of insulating material has total charge Q spread uniformly over its sloping surface. Calculate the work done in bringing a small test charge q from infinity to the apex of the cane. The cone has a slope length L.

Dear ayush,

y/r = x/L => y= xr/L

dq = 2Πydxσ = 2Πrσxdx/l

for this ring potential at vertex = dV = ∫kdq/x

integrating from 0 - L ,
     
         V = 2Πkrσ = Q / 2Πε₀L

Now work done = Vq = Qq / 2Πε₀L

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