Final answer:
The total charge in a spherical shell with specified inner and outer radii and volume charge density is found by computing the volume of the shell and multiplying by the charge density to find the total charge contained.
Step-by-step explanation:
The student's question involves the calculation of the total charge contained within a spherical shell with a given volume charge density. To find this, we must integrate the charge density over the volume of the shell. The shell's volume V can be found by subtracting the volume of the smaller inner sphere from the volume of the larger outer sphere using the formula V = \(\frac{4}{3}\pi (r_2^3 - r_1^3)\), where \(r_1\) and \(r_2\) are the inner and outer radii respectively. Given the volume charge density \(\rho\), the total charge Q within the shell is Q = \(\rho V\).
To calculate this, we first determine the volume of the spherical shell:
V = \(\frac{4}{3}\pi (4.6^3 - 3.4^3)\) cm\(^3\
Therefore, the total charge in a spherical shell with an inner radius of 3.4 cm, outer radius of 4.6 cm, and a volume charge density of 6.4 \(\times\) 10\(^{-4}\) C/m\(^3\) is found to be a specific value of Coulombs, which is the numerical answer to the student's question.