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Question

An extremely long, solid nonconducting cylinder has a radius $R_0$. The charge density within the cylinder is a function of the distance $R$ from the axis, given by $\rho_{\mathrm{E}}(R)=\rho_0\left(R / R_0\right)^2$. What is the electric field everywhere inside and outside the cylinder (far away from the ends) in terms of $\rho_0$ and $R_0$ ?

Solution

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1 of 5Suppose we have a very long non conducting cylinder, with radius of $R_0$ and charge density of $\rho_E(R)=\rho_0 \left(\frac{R}{R_0}\right)^2$, we need to find the electric field inside and out side the cylinder, first, inside the cylinder, draw a Gauss surface (cylinder) inside the original cylinder with radius of $R$ and length of $l$ as shown in the following figure:

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