Question

2. Non-uniform Ball of Charge (20 pts): A spherical charge density is given by Py \rho_{0} r / r_{0} \text { for } 0 \leq r \leq r_{0}, \text {

and } \rho_{v}=0 \text { for } r \geq r_{0} a) Derive an expression for the electric field E for all r. *Hint: Use Gauss's Law. b) Plot E,(r) using MATLAB. c) Find an expression for the electrostatic potential difference V between a point at r = r1 relative to r = r0. You can assume r1 > r0. d) If we replaced the spherical charge density with an equivalent point charge at the origin,we will get the same fields for r > ro. What is this equivalent point charge?

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