Solution Found!
Answer: CALC A nonuniform, but spherically symmetric,
Chapter 22, Problem 22.58(choose chapter or problem)
A nonuniform, but spherically symmetric, distribution of charge has a charge density \(\rho(r)\) given as follows:
\(\rho(r)=\rho_{0}(1-4 r / 3 R) \quad \quad \text { for } r \leq R\)
\(\rho(r)=0 \quad \quad \quad \quad \quad \quad \quad \text{ for } r\ge R\)
where \(\rho_{0}\) is a positive constant. (a) Find the total charge contained in the charge distribution. (b) Obtain an expression for the electric field in the region \(r \geq R\). (c) Obtain an expression for the electric field in the region \(r \leq R\). (d) Graph the electric-field magnitude E as a function of r. (e) Find the value of r at which the electric field is maximum, and find the value of that maximum field.
Questions & Answers
QUESTION:
A nonuniform, but spherically symmetric, distribution of charge has a charge density \(\rho(r)\) given as follows:
\(\rho(r)=\rho_{0}(1-4 r / 3 R) \quad \quad \text { for } r \leq R\)
\(\rho(r)=0 \quad \quad \quad \quad \quad \quad \quad \text{ for } r\ge R\)
where \(\rho_{0}\) is a positive constant. (a) Find the total charge contained in the charge distribution. (b) Obtain an expression for the electric field in the region \(r \geq R\). (c) Obtain an expression for the electric field in the region \(r \leq R\). (d) Graph the electric-field magnitude E as a function of r. (e) Find the value of r at which the electric field is maximum, and find the value of that maximum field.
ANSWER:Step 1 of 8
Given that
