Find the total charge of a cylinder of Radius R and Length L, carrying a charge density that is proportional to the distance from its axis.
∮E⃗dA⃗=qε0,\oint\vec Ed\vec A=\frac q{\varepsilon_0},∮EdA=ε0q,
E(2πr)L=ρπr2Lε0,E(2\pi r)L=\frac{\rho \pi r^2L}{\varepsilon_0},E(2πr)L=ε0ρπr2L,
E=ρr2ε0.E=\frac{\rho r}{2\varepsilon_0}.E=2ε0ρr.
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