Question

A charge of 1.0 × 10-6 μC is located inside a sphere, 1.25 cm from its center. What is the electric flux through the sphere due to this charge?

Answer 1

Answer:

$\Phi_E=0.11\frac{N\cdot m^2}{C}$

Explanation:

According to Gauss's Law, the electric flux of a charged sphere is the electric field multiplied by the area of ​​the spherical surface:

$\Phi_E=EA\\\Phi_E=E(4\pi R^2)\\\Phi_E=\frac{q}{4\pi \epsilon_0 R^2}(4\pi R^2)\\\Phi_E=\frac{q}{\epsilon_0}$

This is identical to the electric flux of a point charge located in the center of the sphere.

$\Phi_E=\frac{1*10^{-12}C}{8.85*10^{-12} \frac{C^2}{N\cdot m^2}}\\\Phi_E=0.11\frac{N\cdot m^2}{C}$

Answer 2

The electric flux through the sphere due to charge is $0.113Nm^{2}/C$

Gauss's Law :

According to Gauss's Law, the electric flux of a charged sphere is the ratio of charge to the electrical permittivity.

• It is given as,  $\phi _{E}=\frac{q}{\epsilon _{0}}$

• Where q is charge in sphere and $\epsilon _{0}$ is permittivity of free space.

• Value of $\epsilon_{0}=8.854*10^{-12} C^{2}/Nm^{2}$

Given that, charge $q=1*10^{-6} \mu C$

Substitute values in flux expression.

                $\phi _{E}=\frac{10^{-6}*10^{-6} }{8.854*10^{-12} } \\\\\phi _{E}=0.113Nm^{2}/C$

Learn more about the electric flux here:

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