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.
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Spandan Senapati
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4 months ago

@Ishan Dixit
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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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Spandan Senapati
·
4 months ago

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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. – Spandan Senapati · 4 months ago

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– Ishan Dixit · 4 months ago

Answer is \(px(\pi*a^2)/2\in\)Log in to reply

– Spandan Senapati · 4 months ago

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 \(1/2\)\(\phi\)Log in to reply

– Ishan Dixit · 4 months ago

but it isnt coming from this method please provide solutionLog in to reply

– Spandan Senapati · 4 months ago

I have provided.If it weren't small then use integration.Log in to reply

– Ishan Dixit · 4 months ago

Thanks got itLog in to reply

– Ishan Dixit · 4 months ago

One thing how does the term R gets sorted ?Log in to reply

– Spandan Senapati · 4 months ago

I have changed it,the variables.Now its fine I guess.Log in to reply

– Ishan Dixit · 4 months ago

But how would the height of small cylinder that is x will come in answerLog in to reply

– Spandan Senapati · 4 months ago

Note that its \(r=x\) and The Radius is \(R=a\).Substitute the variables now.OK?Log in to reply

– Ishan Dixit · 4 months ago

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