The electric field in a region is given $\overrightarrow{ E }=\left(\frac{3}{5} E _{0} \hat{ i }+\frac{4}{5} E _{0} \hat{ j }\right) \frac{ N }{ C } .$ The ratio of flux of reported field through the rectangular surface of area $0.2\, m ^{2}$ (parallel to $y - z$ plane) to that of the surface of area $0.3\, m ^{2}$ (parallel to $x - z$ plane $)$ is $a : b ,$ where $a =$ .............
[Here $\hat{ i }, \hat{ j }$ and $\hat{ k }$ are unit vectors along $x , y$ and $z-$axes respectively]
The electric field in a region is given $\overrightarrow{ E }=\left(\frac{3}{5} E _{0} \hat{ i }+\frac{4}{5} E _{0} \hat{ j }\right) \frac{ N }{ C } .$ The ratio of flux of reported field through the rectangular surface of area $0.2\, m ^{2}$ (parallel to $y - z$ plane) to that of the surface of area $0.3\, m ^{2}$ (parallel to $x - z$ plane $)$ is $a : b ,$ where $a =$ .............
[Here $\hat{ i }, \hat{ j }$ and $\hat{ k }$ are unit vectors along $x , y$ and $z-$axes respectively]
- [JEE MAIN 2021]
- A
$2$
- B
$3$
- C
$4$
- D
$1$
Similar Questions
In $1959$ Lyttleton and Bondi suggested that the expansion of the Universe could be explained if matter carried a net charge. Suppose that the Universe is made up of hydrogen atoms with a number density $N$, which is maintained a constant. Let the charge on the proton be :
${e_p}{\rm{ }} = - {\rm{ }}\left( {1{\rm{ }} + {\rm{ }}y} \right)e$ where $\mathrm{e}$ is the electronic charge.
$(a)$ Find the critical value of $y$ such that expansion may start.
$(b)$ Show that the velocity of expansion is proportional to the distance from the centre.
In $1959$ Lyttleton and Bondi suggested that the expansion of the Universe could be explained if matter carried a net charge. Suppose that the Universe is made up of hydrogen atoms with a number density $N$, which is maintained a constant. Let the charge on the proton be :
${e_p}{\rm{ }} = - {\rm{ }}\left( {1{\rm{ }} + {\rm{ }}y} \right)e$ where $\mathrm{e}$ is the electronic charge.
$(a)$ Find the critical value of $y$ such that expansion may start.
$(b)$ Show that the velocity of expansion is proportional to the distance from the centre.
Give definition of electric flux.
Give definition of electric flux.
A charge is kept at the central point $P$ of a cylindrical region. The two edges subtend a half-angle $\theta$ at $P$, as shown in the figure. When $\theta=30^{\circ}$, then the electric flux through the curved surface of the cylinder is $\Phi$ If $\theta=60^{\circ}$, then the electric flux through the curved surface becomes $\Phi / \sqrt{n}$, where the value of $n$ is. . . . . . .
A charge is kept at the central point $P$ of a cylindrical region. The two edges subtend a half-angle $\theta$ at $P$, as shown in the figure. When $\theta=30^{\circ}$, then the electric flux through the curved surface of the cylinder is $\Phi$ If $\theta=60^{\circ}$, then the electric flux through the curved surface becomes $\Phi / \sqrt{n}$, where the value of $n$ is. . . . . . .
- [IIT 2024]
An infinite line charge is at the axis of a cylinder of length $1 \,m$ and radius $7 \,cm$. If electric field at any point on the curved surface of cylinder is $250 \,NC ^{-1}$, then net electric flux through the cylinder is ............ $Nm ^2 C ^{-1}$
An infinite line charge is at the axis of a cylinder of length $1 \,m$ and radius $7 \,cm$. If electric field at any point on the curved surface of cylinder is $250 \,NC ^{-1}$, then net electric flux through the cylinder is ............ $Nm ^2 C ^{-1}$
Why do two electric field lines not intersect each other ?
Why do two electric field lines not intersect each other ?