The electric field in a region is radially outward with magnitude $E = A{\gamma _0}$. The charge contained in a sphere of radius ${\gamma _0}$ centered at the origin is
The electric field in a region is radially outward with magnitude $E = A{\gamma _0}$. The charge contained in a sphere of radius ${\gamma _0}$ centered at the origin is
- A
$\frac{1}{{4\pi {\varepsilon _0}}}A\gamma _0^3$
- B
$4\pi {\varepsilon _0}A\gamma _0^3$
- C
$\frac{{4\pi {\varepsilon _0}A}}{{{\gamma _0}}}$
- D
$\frac{1}{{4\pi {\varepsilon _0}}}\frac{A}{{\gamma _0^3}}$
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?
The electric field in a region is given by $\vec E = \frac{3}{5}{E_0}\hat i + \frac{4}{5}{E_0}\hat j$ and $E_0 = 2\times10^3\, N/C$. Then, the flux of this field through a rectangular surface of area $0.2\, m^2$ parallel to the $y-z$ plane is......$\frac{{N - {m^2}}}{C}$
The electric field in a region is given by $\vec E = \frac{3}{5}{E_0}\hat i + \frac{4}{5}{E_0}\hat j$ and $E_0 = 2\times10^3\, N/C$. Then, the flux of this field through a rectangular surface of area $0.2\, m^2$ parallel to the $y-z$ plane is......$\frac{{N - {m^2}}}{C}$
If a charge $q$ is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be
If a charge $q$ is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be
- [JEE MAIN 2022]
Draw electric field lines of positive charge.
Draw electric field lines of positive charge.
A point charge $q$ is placed at a distance $a/2$ directly above the centre of a square of side $a$. The electric flux through the square is
A point charge $q$ is placed at a distance $a/2$ directly above the centre of a square of side $a$. The electric flux through the square is