Question

Electric flux through a surface area of $100{m^2}$ lying in the xy plane (in Vm) if $\overrightarrow E = \widehat i + \sqrt 2 \widehat j + \sqrt 3 \widehat k$
A. $100$
B. $141.4$
C. $173.2$
D. $200$

Answer 1

Electric flux through a surface area of $100{m^2}$ lying in the xy plane (in Vm) if Solution: Hint- Electric flux is a way of describing the strength of an electric field at any distance from a charge causing the field. It can also be described as the total number of electric field lines passing through a surface area in unit time.

Formula used
$\phi = \int {\overrightarrow {E.} \widehat nds}$ …………….. (1)
This is known as Gauss’s law, where $\phi$ is the electric flux, $\overrightarrow E$ is the electric field, and $ds$ is the small surface area in which we want to find the flux.

Complete step by step solution:
In question is it given that the electric field lay through xy plane so the electric flux will be in perpendicular direction of the plane so $\widehat n = \widehat k$
And the given surface area $ds = 100{m^2}$
From equation (1)
$\phi = \int {\widehat {(i} + \sqrt 2 \widehat j + \sqrt 3 \widehat k).\widehat k100}$
$\phi = \sqrt 3 \times 100$
$\phi = 1.732 \times 100$
$\phi = 173.2$
So the correct option is (C).

Note:
Electric flux is a measure of the number of electric field lines passing through any surface area. The S.I. unit of electric flux is volt-meter and it is a scalar quantity.
Electric field lines are considered to generate a positive electric charge and to terminate on negative charges. Field lines directed into a closed surface are viewed as negative and the field lines directed out of a closed surface are positive. If the surface has no net charge inside a closed surface, every field line directed into the surface continues through the interior and is directed outward elsewhere on the surface. The negative flux is equivalent in magnitude to the positive flux, so the net or total, electric flux is zero. If a net charge is restrained inside a closed surface, the total flux through the surface is proportional to the enclosed charge, positive if it is positive, negative if it is negative.