Question

3. A spherical shell has an inner radius of 3.7 cm and an outer radius of 4.5 cm. If charge is distributed uniformly throughout the shell with a volume density of 6.1 x I0-4C/m' the total charge is !

Answer 1

The total charge of the shell is about 1.034
`10^(-7)` Coulombs

Step-by-step explanation:

In order to find the actual volume of the spherical shell (
`V_s`), we estimate the volume of the sphere with larger radius R, and subtract from it the volume of the sphere with smaller radius r:

`V_s=(4)/(3) \pi\,R^3-(4)/(3) \pi\,r^3\\V_s=(4)/(3) \pi\,(R^3-r^3)\\V_s=(4)/(3) \pi\,(4.5^3-3.7^3)\,cm^3\\V_s=169.52871 \, cm^3\\V_s=0.00016952871 \, m^3`

Now, in order to find the shell's total charge, we multiply its volume times the volume charge density of the shell (
`6.1\,\,10^(-4)\,(C)/(m^3)`):

`Total\,\,charge=0.00016952871\,m^3\,(6.1\,\,10^(-4)\,(C)/(m^3) = 1.034\,\,10^(-7)\,C`