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Consider a sphere of radius R with harge...

Consider a sphere of radius R with harge density distributed as p(r)=kr fro `r le R=0` for `r gt R`.
(a). Find the electric field as all points r.
(b) Suppose the total charge on the sphere is 2e where e is the electron charge. Where can two protons be embedded such that the force on each of them is zero. Assume that the introduction of the proton does not alter the negative charge distribution.

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To solve the given problem, we will break it down into two parts as specified in the question. ### Part (a): Finding the Electric Field at All Points r 1. **Understanding Charge Density**: The charge density is given as \( \rho(r) = kr \) for \( r \leq R \) and \( \rho(r) = 0 \) for \( r > R \). 2. **Using Gauss's Law**: Gauss's Law states that: \[ ...
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