When does the electric flux associated with a closed surface become positive,zero,or negative?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) The electric flux $\phi$ associated with an area vector $\overrightarrow{S}$ in an electric field $\overrightarrow{E}$ is given by the dot product:
$\phi = \overrightarrow{E} \cdot \overrightarrow{S} = ES \cos \theta$,where $\theta$ is the angle between the electric field vector $\overrightarrow{E}$ and the area vector $\overrightarrow{S}$.
$(i)$ If $\theta = 90^{\circ}$,then $\cos 90^{\circ} = 0$,so $\phi = 0$. This occurs when the electric field lines are parallel to the surface (i.e.,the area vector is perpendicular to the field).
(ii) If $\theta < 90^{\circ}$,then $\cos \theta > 0$,so $\phi > 0$. This occurs when the electric field lines are directed outward from the closed surface.
(iii) If $\theta > 90^{\circ}$,then $\cos \theta < 0$,so $\phi < 0$. This occurs when the electric field lines are directed inward into the closed surface.

Explore More

Similar Questions

$A$ positive charge $q$ is kept at the center of a thick shell of inner radius $R_1$ and outer radius $R_2$ which is made up of conducting material. If $\phi_1$ is the flux through a closed Gaussian surface $S_1$ whose radius is just less than $R_1$ and $\phi_2$ is the flux through a closed Gaussian surface $S_2$ whose radius is just greater than $R_1$,then:

$A$ point charge $q$ is placed at the corner of a cube of side $a$ as shown in the figure. What is the electric flux through the face $ABCD$?

Gauss's law is given by ${\epsilon _0}\oint {\vec E \cdot d\vec s} = q$. If the net charge enclosed by a Gaussian surface is zero,then .......

$A$ square Gaussian surface is placed in the $y-z$ plane. Its axis is along the $x-$axis and its center is at the origin. Two identical charges,each $Q$,are placed at points $(a, 0, 0)$ and $(-a, 0, 0)$. If each side length of the square is $2a$,then the electric flux passing through the square is:

$A$ hemisphere of radius $R$ is placed in a uniform electric field $E$ so that its axis is parallel to the field. Which of the following statement$(s)$ is/are true?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo