Electrostatics

A charge of $4 \,\mu \mathrm{C}$ is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be :

Choose the incorrect statement : (1) The electric lines of force entering into a Gaussian surface provide negative flux. (2) A charge 'q' is placed at the centre of a cube. The flux through all the faces will be the same. (3) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero. (4) When electric field is parallel to a Gaussian surface, it provides a finite non-zero flux. Choose the most appropriate answer from the options given below

Two identical charged particles each having a mass 10 g and charge 2.0 $\times$ 10^$-$7C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.25, find the value of L. [Use g = 10 ms^$-$2]

A long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :

A charged oil drop is suspended in a uniform field of $3 \times {10^4}$ $v/m$ so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge $= 9.9 \times {10^{ - 15}}\,\,kg$ and $g = 10\,m/{s^2}$)

Two point charges $+8q$ and $-2q$ are located at $x=0$ and $x=L$ respectively. The location of a point on the $x$ axis at which the net electric field due to these two point charges is zero is

Assume that an electric field $\overrightarrow E = 30{x^2}\widehat i$ exists in space. Then the potential difference ${V_A} - {V_O},$ where ${V_O}$ is the potential at the origin and ${V_A}$ the potential at $x=2$ $m$ is :

The bob of a simple pendulum has mass 2g and a charge of 5.0 μC. It is at rest in a uniform horizontal electric field of intensity 2000 V/m. At equilibrium, the angle that the pendulum makes with the vertical is : (take g = 10 m/s²)

An electric dipole is placed at an angle of ${30^ \circ }$ to a non-uniform electric field. The dipole will experience

If a charge $q$ is placed at the center of the line joining two equal charges $Q$ such that the system is in equilibrium then the value of $q$ is

A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then $Q/q$ equals:

Two identical positive charges $Q$ each are fixed at a distance of '2a' apart from each other. Another point charge $q_{0}$ with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $\mathrm{q}_{0}$ executes $\mathrm{SHM}$. The time period of oscillation of charge $\mathrm{q}_{0}$ will be :

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of ${30^ \circ }$ with each other. When suspended in a liquid of density $0.8g$ $c{m^{ - 3}},$ the angle remains the same. If density of the material of the sphere is $1.6$ $g$ $c{m^{ - 3}},$ the dielectric constant of the liquid is

Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d\left( {d < < 1} \right)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result charges approach each other with a velocity $v$. Then as a function of distance $x$ between them,

Two charges, each equals to $q,$ are kept at $x=-a$ and $x=a$ on the $x$-axis. A particle of mass $m$ and charge ${q_0} = {q \over 2}$ is placed at the origin. If charge ${q_0}$ is given a small displacement $\left( {y < < a} \right)$ along the $y$-axis, the net force acting on the particle is proportional to

Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between theis F. A third identical conducting sphere, C, is uncharged. Sphere C is first touhed to A, then to B, and then removed. As a result, the force between A and B would be equal to :

Three charges + Q, q, + Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by + Q, placed at x = 0, is zero, then value of q is :

Charge is distributed within a sphere of radius R with a volume charge density $\rho \left( r \right) = {A \over {{r^2}}}{e^{ - {{2r} \over s}}},$ where A and a are constants. If Q is the total charge of this charge distribution, the radius R is :

Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : (m = mass of charged particle)