An infinitely long wire has a uniform linear | vedclass

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

Question

(D) According to Gauss's Law, the net electric flux $\phi$ through a closed surface is given by $\phi = \frac{q_{enc}}{\varepsilon_0}$.The wire passes

Vedclass · Accepted Answer

$2.16$

Vedclass · Answer

(D) According to Gauss's Law, the net electric flux $\phi$ through a closed surface is given by $\phi = \frac{q_{enc}}{\varepsilon_0}$.The wire passes through two maximally displaced corners of the cube, which means it passes along the body diagonal of the cube.The length of the body diagonal of a cube with side length $a$ is $L = \sqrt{3}a$.Given $a = \sqrt{3} \ cm = \sqrt{3} 	imes 10^{-2} \ m$, the length of the wire inside the cube is $L = \sqrt{3} 	imes (\sqrt{3} 	imes 10^{-2} \ m) = 3 	imes 10^{-2} \ m$.The charge enclosed by the cube is $q_{enc} = \lambda \cdot L = (2 	imes 10^{-9} \ C/m) 	imes (3 	imes 10^{-2} \ m) = 6 	imes 10^{-11} \ C$.Using $\frac{1}{4 \pi \varepsilon_0} = 9 	imes 10^9$, we have $\frac{1}{\varepsilon_0} = 36 \pi 	imes 10^9$.Therefore, the flux $\phi = q_{enc} \cdot \frac{1}{\varepsilon_0} = (6 	imes 10^{-11}) 	imes (36 \pi 	imes 10^9) = 216 \pi 	imes 10^{-2} = 2.16 \pi \ Nm^2 C^{-1}$.Thus, $x = 2.16 \pi$.

Similar Questions

$A$ few electric field lines for a system of two charges $Q_1$ and $Q_2$ fixed at two different points on the $x$-axis are shown in the figure. These lines suggest that:-

$A$ charge $Q$ is placed at the centre of a cube of side $a$. The total flux of electric field through the six surfaces of the cube is

$A$ rectangular surface of sides $10 \,cm$ and $15 \,cm$ is placed inside a uniform electric field of $25 \,V/m$,such that the surface makes an angle of $30^{\circ}$ with the direction of the electric field. Find the flux of the electric field through the rectangular surface in $Nm^2/C$.

The charge distribution is shown in the figure below. The electric flux through the surface $S$ due to these charges is .........

$A$ charge $q$ is placed inside a hollow cylinder. The electric flux associated with the curved surface $B$ is $\phi$. The flux associated with a plane surface (either $A$ or $C$) will be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module