Electric Flux

Calculate the electric field intensity at a point, when a sphere of metal has a radius of $12 \mathrm{cm}$ And carries a charge of $1.6\times {10}^{-7}\mathrm{C}$, distributed uniformly on its surface.

(2) $18cm$ From the centre the sphere ?

An electric flux of $-5\times {10}^3 {\mathrm{Nm}}^2{\mathrm{C}}^{-1}$ Passes through a spherical Gaussian surface of radius $20 \mathrm{cm}$ Due to the charge placed at its centre.

(i) Calculate the charge enclosed by the Gaussian surface,

Calculate the number of electric line of force originating from a charge of $1\mathrm{C}$.

If $\overrightarrow{E}=6\hat{i}+3\hat{j}+4\hat{k},$ calculate the electric flux through a surface of area $20$ units in $YZ$ -plane.

The electric field just outside the surface of a conductor has a magnitude $10 \mathrm{kN}/\mathrm{C}$ and is directed away from the conductor. What is the surface charge density of the conductor? 

If an electric field near the earth surface be $300 {\mathrm{Vm}}^{-1}$ directed downwards, what is the surface density on earth's surface?

A point charge produces an electric flux of $-1.0\times {10}^9 {\mathrm{Nm}}^2{\mathrm{C}}^{-1}$ which passes through a Gaussian sphere of radius $10 \mathrm{cm}$ centred on the charge. Compute the point charge. If the radius of the sphere were doubled, how much flux would pass through its surface ?

A thin spherical shell has a radius of $0.5 \mathrm{m}$ carries a charge of $0.2\mu \mathrm{C}.$ Calculate the intensity at point

(i) inside the shell,

A point charge of $2.0\mu \mathrm{C}$ is at the centre of cubic Gaussian surface $9.0 \mathrm{cm}$ on edge. Calculate the net electric flux through the surface,

An uniform electric field of intensity $6\times {10}^3 \mathrm{N}/\mathrm{C}$ is directed along, $X$ -axis. The length and breadth of a rectangular plane surface is $1 \mathrm{m}$ and $0.5 \mathrm{m}$ respectively. Find the electric flux through the surface in the following cases:

(c) the length of the surface is parallel to $Y$-axis, but the normal drawn to it is inclined to the $X$ -axis at an angle of ${60}^{°}$.

Find the electric flux through the surface in the following cases:

An uniform electric field of intensity $6\times {10}^3 \mathrm{N}/\mathrm{C}$ is directed along, $X$ -axis. The length and breadth of a rectangular plane surface is $1 \mathrm{m}$ and $0.5 \mathrm{m}$ respectively.

(ii) When the surface is parallel to $XY$ -plane.

An uniform electric field of intensity $6\times {10}^3 \mathrm{N}/\mathrm{C}$ is directed along, $X$ -axis. The length and breadth of a rectangular plane surface is $1 \mathrm{m}$ and $0.5 \mathrm{m}$ respectively. Find the electric flux through the surface in the following cases:

(1) when the surface is parallel to $YZ$ -plane.

A ring of radius $1 \mathrm{m}$ is placed in an uniform electric field such that the electric flux through it is maximum. If the maximum flux is $2\times {10}^4 {\mathrm{Nm}}^2/\mathrm{C}$, what is the intensity of the electric field? 

A cylinder is placed in uniform electric field $\overrightarrow{E}$ar, with its axis parallel to field. Show that the electric flux through the cylinder is zero.

What is electric flux? What is its unit? What is electric flux density?

Which one (s) of the following statements is/are correct?

A charge $Q$ is distributed uniformly on circular ring of radius $r.$ A sphere of equal radius is constructed with its centre at the periphery of the ring. The flux of the electric field through the surface of the sphere is

A charged ball $B$ hangs from a silk thread $S$ white makes an angle $\theta ,$ with a large charged conducting shut $P,$ as shown in figure, Fig. 3.84. The surface charge density $\sigma$ of the sheet is proportional to

A disc of radius $\frac{a}{4}$ having a uniformly distributed charge $6\mathrm{C}$ is placed in the $x-y$ plane with its centre at $\left(-\frac{a}{2},0,0\right)$ Fig. 3.78. A rod of length $a$ carrying a uniformly distributed

charge $8C$ is placed on the $X-$axis from $x=\frac{a}{4}$ to $x=\frac{5a}{4}$. Two point charges $-7C$ and $3C$ are placed at $\left(\frac{a}{4},-\frac{a}{4},0\right)$ and $\left(-\frac{3a}{4},\frac{3a}{4},0\right)$ respectively. Consider a cubical surface formed by the six surfaces $x=\pm \frac{a}{2},y=\pm \frac{a}{2},z=\pm \frac{a}{2}$. The electric flux through the cubical surface is

The inward and outward electric flux from a closed surface are respectively $8\times {10}^3$ and $4\times {10}^3$ units. Then the net charge inside the closed surface is