Explanation:
(a) Formula to calculate the density is as follows.
[tex]\rho = \frac{Q}{\frac{4}{3}\pi a^{3}}[/tex]
= [tex]\frac{6.50 \times 10^{-6}}{\frac{4}{3} \times 3.14 \times (0.04)^{3}}[/tex]
= [tex]2.42 \times 10^{-2} C/m^{3}[/tex]
Now, calculate the charge as follows.
[tex]q_{in} = \rho(\frac{4}{3} \pi r^{3})[/tex]
= [tex]2.42 \times 10^{-2} C/m^{3} \times 4.1762 \times (0.01)^{3}[/tex]
= [tex]10.106 \times 10^{-8}[/tex] C
or, = 101.06 nC
(b) For r = 6.50 cm, the value of charge will be calculated as follows.
[tex]q_{in} = \frac{Q}{\frac{4}{3}\pi a^{3}}[/tex]
= [tex]\frac{6.50 \times 10^{-6}}{\frac{4}{3} \times 3.14 \times (0.065)^{3}}[/tex]
= 7.454 [tex]\mu C[/tex]
