q_1, q_2, q_3 and q_4 are point charges locat | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) According to Gauss's law,the total electric flux $\Phi_E$ through a closed surface is equal to the total charge enclosed by the surface divided by

Vedclass · Accepted Answer

$\oint\limits_S {\left( {{{\vec E}_1} + {{\vec E}_2} + {{\vec E}_3}} \right) \cdot d\vec A = \frac{{{q_1} + {q_2} + {q_3}}}{{{\epsilon _0}}}}$

Vedclass · Answer

(B) According to Gauss's law,the total electric flux $\Phi_E$ through a closed surface is equal to the total charge enclosed by the surface divided by the permittivity of free space $\epsilon_0$.Mathematically,$\oint\limits_S {\vec E \cdot d\vec A = \frac{{{Q_{enc}}}}{{{\epsilon _0}}}}$.In the given figure,the charges enclosed by the spherical Gaussian surface $S$ are $q_1, q_2,$ and $q_3$. The charge $q_4$ is outside the surface.Therefore,the net electric field $\vec E$ at any point on the surface is the vector sum of the electric fields produced by all charges (both inside and outside),i.e.,$\vec E = \vec E_1 + \vec E_2 + \vec E_3 + \vec E_4$.However,the flux through the surface depends only on the enclosed charge: $\oint\limits_S {\vec E \cdot d\vec A = \frac{{{q_1} + {q_2} + {q_3}}}{{{\epsilon _0}}}}$.Thus,option $B$ is correct.

$q_1, q_2, q_3$ and $q_4$ are point charges located as shown in the figure,and $S$ is a spherical Gaussian surface of radius $R$. Which of the following is true according to Gauss's law?

Similar Questions

Gauss's law should be invalid if

The electric field in a region is given by $\vec E = a\hat i + b\hat j$. Here $a$ and $b$ are constants. Find the net flux passing through a square area of side $l$ parallel to the $y-z$ plane.

For a given surface,the Gauss's law is stated as $\oint {E \cdot ds} = 0$. From this,we can conclude that:

Three positive charges of equal value $q$ are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in:

An infinite line charge is at the axis of a cylinder of length $1 \,m$ and radius $7 \,cm$. If the electric field at any point on the curved surface of the cylinder is $250 \,NC^{-1}$,then the net electric flux through the cylinder is ............ $Nm^2C^{-1}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module