In Example 24 12 you derived the expression for the potential inside a solid sphere of constant charge density by first finding the electric field In this problem you derive the same expression by direct integration Consider a sphere of radius R containing a charge Q uniformly distributed You wish to find V at some point r (a) Find the charge q inside a sphere of radius r and the potential V 1 at r due to this part of the charge (b) Find the potential dV 2 at r due to the charge in a shell of radius r and thickness dr at r r (c) Integrate your expression in (b) from r r to r R to find V 2 (d) Find the total potential V at r from V V 1 V 2 kQ V(r) D (r) 3D 3 R 2R

Question: In Example 24-12 you derived the expression for the potential inside a solid sphere of constant charge density by first finding the electric field. In

In Example 24-12 you derived the expression for the potential inside a solid sphere of constant charge density by first finding the electric field. In this problem you derive the same expression by direct integration. Consider a sphere of radius R containing a charge Q uniformly distributed. You wish to find V at some point r

kQ V(r)%D (r)%3D 3- R? 2R

(a) Find the charge q? inside a sphere of radius r?and the potential V₁ at r?due to this part of the charge.

(b) Find the potential dV₂ at r?due to the charge in a shell of radius r? and thickness dr? at r? > r.

(d) Find the total potential V?at r?from V?= V₁ + V₂.

kQ V(r)%D (r)%3D 3- R? 2R

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