Electric Flux & Gauss's Law

The electric field in the region is $\vec{E} = a\hat{i} + b\hat{j}$ where 'a' and 'b' are constants. The net electric flux passing through a square area of side 'l' parallel to Y-Z plane is

The number of lines of force originating from a point charge of $2 \times 8.85 \times 10^{-9}$ C in a medium of dielectric constant $10$ is ($\epsilon_0 = 8.85 \times 10^{-12}$ SI unit)

The electric flux entering and leaving an enclosed surface are $\Phi_1$ and $\Phi_2$ respectively. The electric charge inside the surface will be ($\varepsilon_0$ = permittivity of vacuum)

A charge 'Q' C is placed at the centre of a cube. The electric flux through two opposite faces of the cube is

($\epsilon_0$ = permittivity of free space)

If the radius of the spherical Gaussian surface is increased then the electric flux due to a point charge enclosed by the surface

Two point charges $8\ \mu\text{C}$ and $-2\ \mu\text{C}$ are located at $x = 2$ cm and $x = 4$ cm, respectively on the $x$-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is ________.

An infinite line charge produces a field of $9 \times 10^{8}$ N/C at a distance of $2$ cm. The linear charge density is

$\left(\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}\right.$ SI unit$\left.\right)$

For a uniformly charged plane sheet, the variation of electric field (E) with distance (d) is correctly shown graphically in graph

The electric field intensity at a point near and outside the surface of a charged conductor of any shape is $E_1$. The electric field intensity due to a uniformly charged infinite thin plane sheet having the same surface charge density is $E_2$. The relation between $E_1$ and $E_2$ is

Which of the following statements are correct?

A. Inside a conductor, the electrostatic field is zero.

B. Electric field at the surface of a charged conductor does not depend on its surface charge density.

C. The interior of a charged conductor can have no excess charge in the static situation. D. At the surface of a charged conductor, the electrostatic field must be normal to the surface at every point.

E. The electrostatic potential is zero everywhere inside a charged conductor.

Choose the correct answer from the options given below:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$

Assertion A: In electrostatics, a conductor does not store any net charge inside. Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift.

Choose the correct answer from the options given below

Two point charges $2q$ and $q$ are placed at vertex $A$ and centre of face $CDEF$ of the cube as shown in figure. The electric flux passing through the cube is:

A spherical conductor of diameter $3$ mm is kept in a uniform electric field of intensity $4 \times 10^{7}$ N/C. The maximum charge on the conductor is $\left(\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\text{ SI units}\right)$

A point charge $Q$ is placed inside a cavity within a solid isolated conducting sphere. Consider points $A, B$ and $C$ as shown in the figure, where the magnitudes of the electric fields are $E_A, E_B, E_C$, respectively. The points $B$ and $C$ are at the same distance from the center of the solid sphere. The correct option is:

The electric flux is $\phi = \alpha\sigma + \beta\lambda$ where $\lambda$ and $\sigma$ are linear and surface charge density, respectively. $\left(\frac{\alpha}{\beta}\right)$ represents

The electric field in a region is given by $\vec{E} = (2\hat{i} + 4\hat{j} + 6\hat{k}) \times 10^{3}\text{ N/C}$. The flux of the field through a rectangular surface parallel to $x - z$ plane is $6.0\text{ N m}^2\text{C}^{-1}$. The area of the surface is _____________ $\text{cm}^2$.

The electric flux through the surface

A charge is uniformly distributed on the surface of a spherical rubber balloon. As it is blown up, the total electric flux coming out of the surface

A charge $Q\ \mu\text{C}$ is placed at the centre of a cube. The flux through two opposite faces of the cube is ( $\varepsilon_0 =$ permittivity of free space)

Four charges $2\ \mu\text{C},\ -3\ \mu\text{C},\ 4\ \mu\text{C},\ -4\ \mu\text{C}$ and $-1\ \mu\text{C}$ are enclosed by the Gaussian surface of radius 2 m. Net outward flux through the Gaussian surface is (in $\mu\text{V-m}$) [ $\varepsilon_0 =$ permittivity of free space]

A hollow cylinder has a charge ' $q$ ' coulomb within it. If ' $\phi$ ' is the electric flux in unit of V-m associated with the curved surface C, the flux linked with the plane surface ' $A$ ' in unit of V-m will be [ $\varepsilon_0 =$ permittivity of free space]0

A hollow cylinder has a charge of ' $q$ ' $C$ within it. If $\phi$ is the electric flux associated with the curved surface B, the flux linked with the plane surface A will be

A point charge causes an electric flux of $-2 \times 10^{4}\text{ N m}^2\text{C}^{-1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is: (Given $\epsilon_0 = 8.85 \times 10^{-12}\text{ C}^2\text{N}^{-1}\text{m}^{-2}$)

The electric field intensity on the surface of a solid charged sphere of radius $\mathbf{r}$ and volume charge density $\sigma$ is ( $\varepsilon_0 =$ permittivity of free space)

The electric field intensity near a conducting surface having uniform surface charge density ' $\sigma$ ' is given by ( $\varepsilon_0 =$ permittivity of free space)

Electric charge is transferred to an irregular metallic disk as shown in the figure. If $\sigma_1, \sigma_2, \sigma_3$ and $\sigma_4$ are charge densities at given points then, choose the correct answer from the options given below:

A. $\sigma_1 > \sigma_3; \sigma_2 = \sigma_4$

B. $\sigma_1 > \sigma_2; \sigma_3 > \sigma_4$

C. $\sigma_1 > \sigma_3 > \sigma_2 = \sigma_4$

D. $\sigma_1 < \sigma_3 < \sigma_2 = \sigma_4$

E. $\sigma_1 = \sigma_2 = \sigma_3 = \sigma_4$

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): The outer body of an aircraft is made of metal which protects persons sitting inside from lightning strikes.

Reason (R): The electric field inside the cavity enclosed by a conductor is zero. In the light of the above statements, choose the most$-$appropriate answer from the options given below:

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density $+\sigma$ and $-2\sigma$. The force experienced by a point charge +q placed at the mid point between two plates will be:

A uniformly charged conducting sphere of diameter 3.5 cm has a surface charge density of $20\ \mu\text{C m}^{-2}$. The total electric flux leaving the surface of the sphere is nearly [permittivity of free space, $\varepsilon_0 = 8.85 \times 10^{-12}\text{ SI}$ unit]

An infinitely long wire has uniform linear charge density $\lambda = 2$ nC/m. The net flux through a Gaussian cube of side length $\sqrt{3}$ cm, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be $x$ Nm${}^{2}\text{C}^{-1}$, where $x$ is:

[Neglect any edge effects and use $\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}$ SI units]

A line charge of length $\frac{a}{2}$ is kept at the center of an edge $BC$ of a cube ABCDEFGH having edge length ' $a$ ' as shown in the figure. If the density of line charge is $\lambda\text{ C}$ per unit length, then the total electric flux through all the faces of the cube will be ___________. (Take, $\epsilon_0$ as the free space permittivity)

A square loop of sides $a = 1\text{ m}$ is held normally in front of a point charge $q = 1\text{ C}$ at a distance $\frac{a}{2}$. The flux of the electric field through the shaded region is $\frac{5}{p} \times \frac{1}{\varepsilon_0}\,\frac{\text{Nm}^{2}}{\text{C}}$, where the value of p is ________.

Two infinite identical charged sheets and a charged spherical body of charge density ' $\rho$ ' are arranged as shown in figure. Then the correct relation between the electrical fields at $A, B, C$ and D points is:

Match List - I with List - II.

Choose the correct answer from the options given below:

An electric field is given by $(6\hat{i} + 5\hat{j} + 3\hat{k})\text{ N/C}$. The electric flux through a surface area $30\hat{i}\text{ m}^2$ lying in YZ-plane (in SI unit) is:

An electric field, $\vec{E} = \frac{2\hat{i} + 6\hat{j} + 8\hat{k}}{\sqrt{6}}$ passes through the surface of $4\text{ m}^2$ area having unit vector $\hat{n} = \left(\frac{2\hat{i} + \hat{j} + \hat{k}}{\sqrt{6}}\right)$. The electric flux for that surface is _________ $\text{V m}$.

A hollow cylinder has charge ' $q$ ' $C$ within it. If ' $\phi$ ' is the electric flux associated with the curved surface B, the flux linked with the plane surface A will be:

The electric flux over a sphere of radius ' $r$ ' is ' $\phi$ '. If the radius of the sphere is doubled without changing the charge, the flux will be

If the electric flux entering and leaving an enclosed surface is $\phi_1$ and $\phi_2$ then charge enclosed in the surface is ($\varepsilon_0 =$ permittivity of free space)

Two surfaces A and B are enclosing the charges as shown below. The total normal electric induction (T.N.E.I) through the surfaces A and B are respectively.

A spherical rubber balloon carries a charge, uniformly distributed over the surface. As the balloon is blown up and increases in size, the total electric flux coming out of the surface

If the electric flux entering and leaving an enclosed surface are $\phi_1$ and $\phi_2$ respectively, the electric charge inside the surface will be

Five charges $+q, +5q, -2q, +3q$ and $-4q$ are situated as shown in the figure. The electric flux due to this configuration through the surface $S$ is:

A charge $q$ is placed at the center of one of the surfaces of a cube. The flux linked with the cube is:

$C_1$ and $C_2$ are two hollow concentric cubes enclosing charges $2Q$ and $3Q$ respectively as shown in figure. The ratio of electric flux passing through $C_1$ and $C_2$ is:

Two charges of $5Q$ and $-2Q$ are situated at the points $(3a, 0)$ and $(-5a, 0)$ respectively. The electric flux through a sphere of radius '$4a$' having center at origin is:

$\sigma$ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is:

The van de Graaff Generator is not based on

The vehicles carrying inflammable fluids usually have metallic chains touching the ground:

An electric field $\vec{E} = (2x\hat{i})\text{ NC}^{-1}$ exists in space. A cube of side $2\text{ m}$ is placed in the space as per figure given below. The electric flux through the cube is ______ $\text{Nm}^{2}/\text{C}$.

A uniformly charged conducting sphere of diameter 14 cm has surface charge density of $40\ \mu\text{C m}^{-2}$. The total electric flux leaving the surface of the sphere is nearly (Permittivity of free space $= 8.85 \times 10^{-12}$ SI unit)

Consider a long uniformly charged cylinder having constant volume charge density ' $\lambda$ ' and radius ' $R$ '. A Gaussian surface is in the form of a cylinder of radius ' $r$ ' such that vertical axis of both the cylinders coincide. For a point inside the cylinder $(r < R)$, electric field is directly proportional to

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $P$ is $\frac{x\sigma}{\epsilon_0}$. The value of $x$ is _________ (all quantities are measured in SI units).

An infinite plane sheet of charge having uniform surface charge density $+\sigma_s\text{ C/m}^{2}$ is placed on $x\text{-}y$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda_e\text{ C/m}$ is placed at $z = 4\text{ m}$ plane and parallel to $y$-axis. If the magnitude values $|\sigma_s| = 2|\lambda_e|$ then at point $(0, 0, 2)$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi\sqrt{n} : 1$. The value of $n$ is _________.

According to Gauss law of electrostatics, electric flux through a closed surface depends on:

A charge $Q\ \mu\text{C}$ is placed at the centre of a cube. The flux coming out from any one of its faces will be (in SI unit):

If $\oint_s \vec{E} \cdot \overrightarrow{dS} = 0$ over a surface, then:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: If an electric dipole of dipole moment $30 \times 10^{-5}\text{ C m}$ is enclosed by a closed surface, the net flux coming out of the surface will be zero.

Reason R: Electric dipole consists of two equal and opposite charges.

In the light of the above statements, choose the correct answer from the options given below.

A charge $17.7 \times 10^{-4}\text{ C}$ is distributed uniformly over a large sheet of area $200\text{ m}^2$. The electric field intensity at a distance $20\text{ cm}$ from it in air will be $\left[\varepsilon_0 = 8.85 \times 10^{-12}\text{ C}^2/\text{N m}^2\right]$

The electric field intensity on the surface of a solid charged sphere of radius '$r$' and volume charge density '$\rho$' is ($\varepsilon_0 =$ permittivity of free space)

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $R$, with distance $r$ from the centre O is represented by:

Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different regions $E_{I}, E_{II}$ and $E_{III}$ are:

Which of the following statements is 'WRONG' for the conductors?

As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $Q$ in three different regions $\text{I, II}$ and $\text{III}$ is given by:

$(\text{I}: r < a, \text{II}: a < r < b$, III: $r > b$)

A cubical volume is bounded by the surfaces $x = 0, x = a, y = 0, y = a, z = 0, z = a$. The electric field in the region is given by $\vec{E} = E_0 x\hat{i}$. Where $E_0 = 4 \times 10^{4}\text{ NC}^{-1}\text{ m}^{-1}$. If $a = 2\text{ cm}$, the charge contained in the cubical volume is $Q \times 10^{-14}\text{ C}$. The value of $Q$ is ________________. (Take $\epsilon_0 = 9 \times 10^{-12}\text{ C}^{2}/\text{Nm}^{2}$)

Expression for an electric field is given by $\vec{E} = 4000x^{2}\hat{i}\ \frac{\text{V}}{\text{m}}$. The electric flux through the cube of side $20\text{ cm}$ when placed in electric field (as shown in the figure) is __________ $\text{V cm}$.

In a cuboid of dimension $2L \times 2L \times L$, a charge $q$ is placed at the center of the surface '$S$' having area of $4L^{2}$. The flux through the opposite surface to '$S$' is given by

As shown in figure, a cuboid lies in a region with electric field $E = 2x^{2}\hat{i} - 4y\hat{j} + 6\hat{k}\text{ N/C}$. The magnitude of charge within the cuboid is $n\epsilon_0\text{ C}$.

The value of $n$ is _________ (if dimension of cuboid is $1 \times 2 \times 3\text{ m}^{3}$)

A thin infinite sheet charge and an infinite line charge of respective charge densities $+\sigma$ and $+\lambda$ are placed parallel at $5\text{ m}$ distance from each other. Points 'P' and 'Q' are at $\frac{3}{\pi}$ m and $\frac{4}{\pi}$ m perpendicular distances from line charge towards sheet charge, respectively. '$E_P$ ' and '$E_Q$' are the magnitudes of resultant electric field intensities at point 'P' and 'Q', respectively. If $\frac{E_P}{E_Q} = \frac{4}{a}$ for $2|\sigma| = |\lambda|$, then the value of $a$ is ___________.

A conducting sphere of radius $0.1\text{ m}$ has uniform charge density $1.8\ \mu\text{C/m}^{2}$ on its surface. The electric field in free space at radial distance $0.2\text{ m}$ from a point on the surface is ( $\varepsilon_0 =$ permittivity of free space)

A solid metallic sphere has a charge $+3Q$. Concentric with this sphere is a conducting spherical shell having charge $-Q$. The radius of the sphere is '$A$' and that of the spherical shell is '$B$'. $(B > A)$. The electric field at a distance '$R$' $(A < R < B)$ from the centre is ( $\varepsilon_0 =$ permittivity of vacuum)

If the radius of the spherical gaussian surface is increased then the electric flux due to a point charge enclosed by the surface

In the figure, a very large plane sheet of positive charge is shown. P1 and P2 are two points at distance l and 2l from the charge distribution. If $\sigma$ is the surface charge density, then the magnitude of electric fields E1 and E2 at P1 and P2 respectively are:

A long cylindrical volume contains a uniformly distributed charge of density $\rho\text{ C m}^{-3}$. The electric field inside the cylindrical volume at a distance $x = \frac{2\varepsilon_0}{\rho}\text{ m}$ from its axis is ________ $\text{V m}^{-1}$.

Given below are two statements.

Statement I: Electric potential is constant within and at the surface of each conductor. Statement II: Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.

In the light of the above statements, choose the most appropriate answer from the options given below.

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:

The volume charge density of a sphere of radius $6\text{ m}$ is $2\ \mu\text{C cm}^{-3}$. The number of lines of force per unit surface area coming out from the surface of the sphere is _______________ $\times 10^{10}\text{ NC}^{-1}$. [Given: Permittivity of vacuum $\epsilon_0 = 8.85 \times 10^{-12}\text{ C}^{2}\text{ N}^{-1}\text{-m}^{-2}$ ]

A spherically symmetric charge distribution is considered with charge density varying as $\rho(r) = \rho_0\left(\frac{3}{4} - \frac{r}{R}\right)$ for $r \leq R$

zero for $r > R$

Where, $r\,(r < R)$ is the distance from the centre O (as shown in figure). The electric field at point P will be: