Question

What is the electric flux through a sphere that has a radius of 1.00

m and carries a charge of +1.00

`{10}^( - 6)`
C at its center?​

Answer 1

E = 8991.8 N/C

Step-by-step explanation:

To find the electric flux in the sphere you use the Gaussian formula:

`\int \vec{E}d\vec{A}=(Q)/(\epsilon_o)`

but, electric field is given by

`E=(Q)/(4\pi \epsilon_o r^2)`

in each point of the sphere surface, electric field is parallel to the normal vector of the surface:

`E\int d \vec{A}=E(4\pi r^2)\\\\E(4\pi r^2)=(Q)/(\epsilon_o)\\\\E=(Q)/(4\pi \epsilon_o r^2)\\\\`

Then, for r = 1.00 m you have:

`E=(1*10^(-6)C)/(4\pi (1.00m)^2(8.85*10^(-12)C^2/Nm^2))=8991.8(N)/(C)`

where you have used that εo = 8.85*10^-12 C^2/Nm^2