Answer:
E = 8991.8 N/C
Explanation:
To find the electric flux in the sphere you use the Gaussian formula:
[tex]\int \vec{E}d\vec{A}=\frac{Q}{\epsilon_o}[/tex]
but, electric field is given by
[tex]E=\frac{Q}{4\pi \epsilon_o r^2}[/tex]
in each point of the sphere surface, electric field is parallel to the normal vector of the surface:
[tex]E\int d \vec{A}=E(4\pi r^2)\\\\E(4\pi r^2)=\frac{Q}{\epsilon_o}\\\\E=\frac{Q}{4\pi \epsilon_o r^2}\\\\[/tex]
Then, for r = 1.00 m you have:
[tex]E=\frac{1*10^{-6}C}{4\pi (1.00m)^2(8.85*10^{-12}C^2/Nm^2)}=8991.8\frac{N}{C}[/tex]
where you have used that εo = 8.85*10^-12 C^2/Nm^2
