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## Homework Statement

A solid insulating cone has a uniform charge density of rho and a total charge of Q. The base of teh cone had a radius of R and a height of h. We wish to find the electric force on a point charge of q' at point A, located at the tip of the cone. (Hint: You may use the result of the electric force along the axis of a disk when solving this problem.)

## Homework Equations

[

[itex]E= \frac{Q}{2\pi \epsilon_{0} R^{2} }(1 -\frac{z}{ (z^{2}+R^{2}) ^{1/2} })[/itex]

## The Attempt at a Solution

I decide to lay the cone flat along the z axis. My calculations are independent of the coordinate system though ( which I think may be wrong). I choose a flat disc(area of a circle) for my charge element dQ.

[itex] \rho = \frac{Q}{V}[/itex]

[itex]dq = \rho \pi r^{2}[/itex]

[itex]dF = \frac{\rho \pi r^{2}dr}{4\pi \epsilon_{0}h^{2}}[/itex]

[itex]F = \frac{\rho \pi}{4\pi \epsilon_{0}h^{2}}\int^{0}_{R}r^{2}dr[/itex]

[itex]F = \frac{-\rho\pi R^{3}}{12\pi \epsilon_{0}H^{2}}[/itex]

[itex]F = \frac{-Q R^{3}}{12\pi \epsilon_{0}H^{4}}[/itex]

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