Answer:
The sphere's volume charge density is 2.58 μC/m³.
Explanation:
Given that,
Radius of sphere R= 8.40 cm
Electric field [tex]E= 2.04\times10^{3}\ N/C[/tex]
Distance r= 16.8 cm
We need to calculate the sphere's volume charge density
Using Gauss's law
[tex]\int{\vec{E}\cdot\vec{da}}=\dfrac{Q_{enc}}{\epsilon_{0}}[/tex]
[tex]E\times 4\pi r^2=\dfrac{1}{\epsilon_{0}}\times\dfrac{4}{3}\piR^3\rho[/tex]
[tex]E=\dfrac{\rho R^3}{3\epsilon_{0}r^2}[/tex]
[tex]\rho=\dfrac{3\times E\times\epsilon_{0}r^2}{R^3}[/tex]
Put the value into the formula
[tex]\rho=\dfrac{3\times2.04\times10^{3}\times8.85\times10^{-12}\times(16.8\times10^{-2})^2}{(8.40\times10^{-2})^3}[/tex]
[tex]\rho=2.58\times10^{-6}\ C/m^3[/tex]
[tex]\rho=2.58\ \mu C/m^3[/tex]
Hence, The sphere's volume charge density is 2.58 μC/m³.
