The electric field in a region is given $\vec E = a\hat i + b\hat j$ . Here $a$ and $b$ are constants. Find the net flux passing through a square area of side $l$ parallel to $y-z$ plane
The electric field in a region is given $\vec E = a\hat i + b\hat j$ . Here $a$ and $b$ are constants. Find the net flux passing through a square area of side $l$ parallel to $y-z$ plane
- A
$al^2$
- B
$bl^2$
- C
Zero
- D
$(a + b)\,l^2$
Similar Questions
An electric field is uniform, and in the positive $x$ direction for positive $x,$ and uniform with the same magnitude but in the negative $x$ direction for negative $x$. It is given that $E =200 \hat{ i }\; N/C$ for $x\,>\,0$ and $E = - 200\hat i\;N/C$ for $x < 0 .$ A right ctrcular cyllnder of length $20 \;cm$ and radius $5\; cm$ has its centre at the origin and its axis along the $x$ -axis so that one face is at $x=+10\; cm$ and the other is at $x=-10\; cm$
$(a)$ What is the net outward flux through each flat face?
$(b)$ What is the flux through the side of the cylinder?
$(c)$ What is the net outward flux through the cylinder?
$(d)$ What is the net charge inside the cyllnder?
An electric field is uniform, and in the positive $x$ direction for positive $x,$ and uniform with the same magnitude but in the negative $x$ direction for negative $x$. It is given that $E =200 \hat{ i }\; N/C$ for $x\,>\,0$ and $E = - 200\hat i\;N/C$ for $x < 0 .$ A right ctrcular cyllnder of length $20 \;cm$ and radius $5\; cm$ has its centre at the origin and its axis along the $x$ -axis so that one face is at $x=+10\; cm$ and the other is at $x=-10\; cm$
$(a)$ What is the net outward flux through each flat face?
$(b)$ What is the flux through the side of the cylinder?
$(c)$ What is the net outward flux through the cylinder?
$(d)$ What is the net charge inside the cyllnder?
A disk of radius $a / 4$ having a uniformly distributed charge $6 C$ is placed in the $x-y$ plane with its centre at $(-a / 2,0,0)$. A rod of length $a$ carrying a uniformly distributed charge $8 C$ is placed on the $x$-axis from $x=a / 4$ to $x=5 a / 4$. Two point charges $-7 C$ and $3 C$ are placed at $(a / 4,-$ $a / 4,0)$ and $(-3 a / 4,3 a / 4,0)$, respectively. Consider a cubical surface formed by six surfaces $x=\pm a / 2, y=\pm a / 2, z=\pm a / 2$. The electric flux through this cubical surface is
A disk of radius $a / 4$ having a uniformly distributed charge $6 C$ is placed in the $x-y$ plane with its centre at $(-a / 2,0,0)$. A rod of length $a$ carrying a uniformly distributed charge $8 C$ is placed on the $x$-axis from $x=a / 4$ to $x=5 a / 4$. Two point charges $-7 C$ and $3 C$ are placed at $(a / 4,-$ $a / 4,0)$ and $(-3 a / 4,3 a / 4,0)$, respectively. Consider a cubical surface formed by six surfaces $x=\pm a / 2, y=\pm a / 2, z=\pm a / 2$. The electric flux through this cubical surface is
A cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by-
A cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by-
An electric line of force in the $xy$ plane is given by equation ${x^2} + {y^2} = 1$. A particle with unit positive charge, initially at rest at the point $x = 1,\;y = 0$ in the $xy$ plane
An electric line of force in the $xy$ plane is given by equation ${x^2} + {y^2} = 1$. A particle with unit positive charge, initially at rest at the point $x = 1,\;y = 0$ in the $xy$ plane
- [IIT 1988]
Choose the incorrect statement :
$(a)$ The electric lines of force entering into a Gaussian surface provide negative flux.
$(b)$ A charge ' $q$ ' is placed at the centre of a cube. The flux through all the faces will be the same.
$(c)$ In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero.
$(d)$ When electric field is parallel to a Gaussian surface, it provides a finite non-zero flux.
Choose the most appropriate answer from the options given below
Choose the incorrect statement :
$(a)$ The electric lines of force entering into a Gaussian surface provide negative flux.
$(b)$ A charge ' $q$ ' is placed at the centre of a cube. The flux through all the faces will be the same.
$(c)$ In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero.
$(d)$ When electric field is parallel to a Gaussian surface, it provides a finite non-zero flux.
Choose the most appropriate answer from the options given below
- [JEE MAIN 2021]