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Note by Ishan Dixit
4 months ago

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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. · 4 months ago

Answer is $$px(\pi*a^2)/2\in$$ · 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 $$1/2$$$$\phi$$ · 4 months ago

but it isnt coming from this method please provide solution · 4 months ago

I have provided.If it weren't small then use integration. · 4 months ago

Thanks got it · 4 months ago

One thing how does the term R gets sorted ? · 4 months ago

I have changed it,the variables.Now its fine I guess. · 4 months ago

But how would the height of small cylinder that is x will come in answer · 4 months ago

Note that its $$r=x$$ and The Radius is $$R=a$$.Substitute the variables now.OK? · 4 months ago