729 small identical spheres each charged to an electric potential 3V combine to form a bigger sphere. The electric potential of the bigger sphere is

The electric field due to an infinitely long thin straight wire with uniform linear charge density of $2.5 \times 10^{-7} \mathrm{~cm}^{-1}$ at a radial distance of $x$ from the wire is $7.5 \times 10^4 \mathrm{NC}^{-1}$. Then, $x=$

An alpha particle and a proton are accelerated from rest in a uniform electric field. The ratio of the times taken by proton and alpha particle to attain equal displacements is

Four electric charges $2 \mu \mathrm{C}, Q, 4 \mu \mathrm{C}$ and $12 \mu \mathrm{C}$ are placed on $X$-axis at distance $x=0,1 \mathrm{~cm}, 2 \mathrm{~cm}$ and 4 cm respectively. If the net force acting on the charge at origin is zero, then $Q=$

If a particle of mass 10 mg and charge $2 \mu \mathrm{C}$ at rest is subjected to a uniform electric field of potential difference 160 V , then the velocity acquired by the particle is

An electron and a positron enter a uniform electric field $E$ perpendicular to it with equal speeds at the same time. The distance of separation between them in the direction of the field after a time ' $t$ ' is

( $\frac{e}{m}$ is specific charge of electron)

A charge $q$ is placed at the centre ' $O$ ' of a circle of radius $R$ and two other charges $q$ and $q$ are placed at the ends of the diameter $A B$ of the circle. The work done to move the charge at point $B$ along the circumference of the circle to a point $C$ as shown in the figure is

For any fixed distance, the electromagnetic force between two protons is $10^n$ times of the gravitational force between them. Then, $n=$

A thin spherical shell of radius $R$ and surface charge density $\sigma$ is placed in a cube of side $5 R$ with their centers coinciding. The electric flux through one face of the cube is $\left(\varepsilon_0=\right.$ Permittivity of free space $)$

A hollow spherical shell of radius $r$ has a uniform charge density $\sigma$. It is kept in a cube of edge $3 r$ such that the centres of the cube and the shell coincide. Then the electric flux coming out of one face of a cube is ( $\varepsilon_0=$ permittivity of free space)

If the electric potential at a point on the surface of a hollow conducting sphere of radius $R$ is $V$, then the electric potential at a point which is at distance $R / 3$ from the centre of the sphere is

The ratio of relative strengths of the gravitational force and the electromagnetic force between two charged particles is

Two conducting spheres of radii $r_1$ and $r_2$ are charged to the same surface charge density. The ratio of electric fields near their surfaces is

Two electric charges $+2 \mu \mathrm{C}$ and $-4 \mu \mathrm{C}$ are separated by a distance 3 m in air. At a point $P$ located on the line joining the two charges and in between them, the electric potential is zero. Then the electric field at a point $P$ (in $\mathrm{NC}^{-1}$ ) is

The flux of the electric field $\mathbf{E}=24 \hat{\mathbf{i}}+30 \hat{\mathbf{j}}+28 \hat{\mathbf{k}} \mathrm{NC}^{-1}$ through an area of $20 \mathrm{~m}^2$ on the $Y Z$-plane is

A small block of mass 5 g and charge $5 \mu \mathrm{C}$ is placed on insulated, frictionless, inclined plane of angle $60^{\circ}$. An electric field is applied parallel to the inclined plane. If the block remains at rest, then the magnitude of electric field is (take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

Two metal spheres have their radii in the ratio of $4: 7$. They are put in contact and a charge $8.8 \times 10^{-7} \mathrm{C}$ is given to the system. Then they are separated, so that each can exert no influence on the other. The potential due to the smaller sphere at 60 m from it in V is

Two charges are $+10 \mu \mathrm{C}$ and $-10 \mu \mathrm{C}$ are separated by 10 cm . The magnitude of force acting on another charge $5 \mu \mathrm{C}$ placed at the mid-point of the line joining the two charges will be (use, $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9$ in SI unit)

A sphere-1 with redius $R$ has charge $q$. Sphere-2 with radius $3 R$ is far from sphere-1 and is initially uncharged. If the two spheres are now connected with a thin conducting wire, then the ratio $\frac{\sigma_1}{\sigma_2}$ of the surface charge densities is

$6 \mu \mathrm{C}$ charge is placed at the centre of a cube. What will be the electric flux at each face of the cube?

$ \left[\text { Take, } \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{~N}-\mathrm{m}^2 \mathrm{C}^2\right] $

There are two thin wire rings, each of radius $R$, whose axes coincide. The charges of the rings are $q$ and $-q$. The magnitude of potential difference between the centres of the rings separated by a distance $\sqrt{3} R$ is

Two charged particles of mass 1 g each are placed 1 m apart. If each of these possesses 1 femto coulomb of charge, then the dominant force of interaction between them is

Three charges are arranged on the vertices of a right angle triangle as shown in the figure. The magnitude of dipole moment of the combination in the unit of $\mathrm{C}-\mathrm{cm}$ is

A particle of mass $m$ and charge $q$ travelling with a velocity $v$ along the $X$-axis enters a uniform electric field $\mathbf{E}$ directed along the $Y$-axis. What will be the trajectory of the particle?

A large metal plate has a surface charge density of $8.85 \times 10^{-6} \mathrm{C} / \mathrm{m}^2$. An electron having initial kinetic energy of $8 \times 10^{-17} \mathrm{~J}$ is moving towards the centre of the plate. If the electron stops just before reaching the plate, then the initial distance between the electron and the plate is

[take $\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{N}-\mathrm{m}^2$ ]

An electron is released from a distance of 4 m from a stationary point charge 20 nC . What will be the speed of the electron, when it is

2 m away from the point charge?

(Charge of electron $=1.6 \times 10^{-19} \mathrm{C}$, mass of electron

$ =9 \times 10^{-31} \mathrm{~kg}, \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \text { SI unit) } $

105. The electric flux from a cube of edge $l$ is $\phi$ in an enclosed charge. If the edge of the cube is made $\frac{2}{3} l$ and the charge enclosed in the cube is doubled, then the electric flux value will be

106. If the dielectric constant of a substance $K=\frac{4}{3}$, then the electric susceptibility $\chi$ in terms of vacuum permittivity $\varepsilon_0$ is

In a uniformly charged sphere of total charge $Q$ and radius $R$, the electric field $E$ is plotted as function of distance from the centre of the sphere. The graph which would correspond to the above description will be

Electric charges $+q$ and $-q$ are placed at points $A$ and $B$ respectively which are at a distance of $2 L$ apart. If $C$ is the midpoint between $A$ and $B$, then the work done in moving a charge $+Q$ along the semi-circle $C R D$ is

Two negative charges of equal magnitude are located in $x y$-plane as shown below in the figure. The direction of the electric field at point $P$ is

An infinite non-conducting sheet has a surface charge density $2 \times 10^{-7} \mathrm{C} / \mathrm{m}^2$ on one side. The distance between two equipotential surfaces whose potential differ by 90 V is (assume, $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \frac{\mathrm{Nm}^2}{\mathrm{C}^2}$ )

If a proton is moved against the coulomb force of an electric field, then