Question

Define and give Gauss' theorem.

Answer 1

Explanation:

Q is the charge enclosed by a surface, epsilon-zero is the permittivity of free space, which is just a constant that is always equal to 8.85 x 10^-12, and phi is the electric flux through the surface. ... So for example, you could use Gauss' Law to figure out the electric field created by a charged conducting sphere.

Answer 2

EXPLANATION.

GAUSS LAW.

The total electric flux through a closed surface (3-D surface) is $\sf \dfrac{1}{\epsilon_o}$ time the net charge enclosed by the surfaces.

$\sf \implies \phi_n_e_t = \dfrac{q_i_n_s_i_d_e}{\epsilon_o}$

$\sf \implies \phi_n_e_t = \dfrac{q}{\epsilon_o}$

$\sf \implies d\phi = \vec{E}.\vec{dA}$

$\sf \implies d\phi = EdA cos(0)$

$\sf \implies d\phi= EdA.$

$\sf \implies \phi_n_e_t = \oint d\phi = \oint EdA$

$\sf \implies \phi_n_e_t = E \oint dA = E \times 4\pi R^{2}$

$\sf \implies \dfrac{KQ}{R^{2} } \times 4\pi R^{2}$

$\sf \implies \dfrac{Q}{4\pi \epsilon_o} \times 4\pi = \dfrac{q}{\epsilon_o}$