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# A cone made of insulating material has a 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 cone. The cone has a slope length L.

Arun Kumar IIT Delhi
7 years ago
Let the angle between the cone is
$2\theta$
Every charged particle on the Cone is has a force on q but force along the direction toward the center is not cancelled and others are. Try to visualize in case you feel problem.
Hieght of the cone =h
distance of particle =x
$dE_{total}=E_{ring}=kqdQz/(z^2+R^2)^{3/2} \\R=lsin(\theta)\\ dQ=2\pi R*dl/\pi r_{cone}L \\=>dQ=2ldl/L \\=>dE_{total}=E_{ring}=lkq2dlz/(z^2+(lsin(\theta))^2)^{3/2}$
integrate from 0 to L for charge q at a distance z which is constant.

Then Integrate the integrated
$(\infty \to Lsin(\theta) )$

`Thanks & RegardsArun KumarIIT DelhiAskiitians Faculty`