Electrostatics> A cone made of insulating material has a ...

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.

Harsh Srivastava , 10 Years ago

Grade 11

1 Answers

Arun Kumar

Last Activity: 10 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 & Regards
Arun Kumar
IIT Delhi
Askiitians Faculty

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Electrostatics> A cone made of insulating material has a ...

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.

Harsh Srivastava , 10 Years ago

Arun Kumar

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