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Using gauss theorem you can easily find the dependence of field on $r$ the distance from the axis.For this use $E2πrh=\rhoπr^2h$.The net flux through the part(cylinder) is $Q/\epsilon$.Now this is equal to $\phi1$+$\phi2$.To find $\phi2$ or the flux through the circular face use the very definition of flux $\phi$=$EdScos\alpha$.And note that the field that we computed is radially outwards.An important aspect to note is that one can't use Solid Angle here as the field dependence isn't $1/r^2$.So use the trivial method.

Yes its correct.Another thing worth noting is small circular face So we can neglect the small angle $\alpha-->0$.So $\phi2$=$EπR^2$=$\rho r/2\epsilon*πR^2$.And Subtract this from $\phi$=$\rho πR^2r/\epsilon$.The answer comes to be $1/2$$\phi$

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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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TopNewestUsing gauss theorem you can easily find the dependence of field on $r$ the distance from the axis.For this use $E2πrh=\rhoπr^2h$.The net flux through the part(cylinder) is $Q/\epsilon$.Now this is equal to $\phi1$+$\phi2$.To find $\phi2$ or the flux through the circular face use the very definition of flux $\phi$=$EdScos\alpha$.And note that the field that we computed is radially outwards.An important aspect to note is that one can't use Solid Angle here as the field dependence isn't $1/r^2$.So use the trivial method.

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Answer is $px(\pi*a^2)/2\in$

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but it isnt coming from this method please provide solution

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$r=x$ and The Radius is $R=a$.Substitute the variables now.OK?

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Yes its correct.Another thing worth noting is small circular face So we can neglect the small angle $\alpha-->0$.So $\phi2$=$EπR^2$=$\rho r/2\epsilon*πR^2$.And Subtract this from $\phi$=$\rho πR^2r/\epsilon$.The answer comes to be $1/2$$\phi$

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