Electrostatics

A simple pendulum of length $l$ has a bob of mass $m$ ，with a charge $q$ ．On it a vertical sheet of charge， with surface charge density＇$\sigma$＇passes through the point of suspension．At equilibrium，if the string makes an angle $\theta$ wit...

Two charges $+q$ and $-q$ are placed at points $A$ and $B$ respectively which are at a distance $2 L_{\mathrm{p} p a t}$ $C$ is the mid point of $A$ and $B$. The workdone in moving a charge $+Q$ along the semicircle $\operatorname{CSD}\left...

Consider a particle of mass 1 gm and charge 1.0 Coulomb is at rest. Now the particle is subjected to an electric field $E(t)=E_0 \sin \omega t$ in the $x$-direction, where $E_0=2$ Newton/Coulomb and $\omega=1000 \mathrm{rad} / \mathrm{sec}$...

A charge Q is placed at the centre of a cube of sides a. The total flux of electric field through the six surfaces of the cube is

Three point charges \(\mathrm{q},-2 \mathrm{q}\) and \(\mathrm{q}\) are placed along \(x\) axis at \(x=-{a}, 0\) and $a$ respectively. As \(\mathrm{a} \rightarrow 0\) and \(\mathrm{q} \rightarrow \infty\) while $$\mathrm{q} \mathrm{a}^2=\ma...

Consider the integral form of the Gauss' law in electrostatics
\(\oint {\overrightarrow E .d\overrightarrow S } = {Q \over {{\varepsilon _0}}}\)
Which of the following statements are correct?

An electric dipole of dipole moment \(\vec{p}\) is placed at the origin of the co-ordinate system along the \(\mathrm{z}\)-axis. The amount of work required to move a charge '\(\mathrm{q}\)' from the point \((\mathrm{a}, 0, 0)\) to the poin...

The figure represents two equipotential lines in x-y plane for an electric field. The x-component E\(_x\) of the electric field in space between these equipotential lines is,

A thin glass rod is bent in a semicircle of radius R. A charge is non-uniformly distributed along the rod with a linear charge density \(\lambda=\lambda_0\sin\theta\) (\(\lambda_0\) is a positive constant). The electric field at the centre...

Consider a positively charged infinite cylinder with uniform volume charge density \(\rho > 0\). An electric dipole consisting of + Q and \(-\) Q charges attached to opposite ends of a massless rod is oriented as shown in the figure. At th...

A hemisphere of radius R is placed in a uniform electric field E so that its axis is parallel to the field. Which of the following statement(s) is/are true?

Consider two concentric conducting sphere of radii R and 2R respectively. The inner sphere is given a charge +Q. The other sphere is grounded. The potential at \(r = {{3R} \over 2}\) is

A neutral conducting solid sphere of radius R has two spherical cavities of radius a and b as shown in the figure. Centre to centre distance between two cavities is c. qa and qb charges are placed at the centres of cavities respectively. T...

Two charges, each equal to \(-\)q are kept at (\(-\)a, 0) and (a, 0). A charge q is placed at the origin. If q is given a small displacement along y direction, the force acting on q is proportional to

The electric potential for an electric field directed parallel to X-axis is shown in the figure. Choose the correct plot of electric field strength.

Two point charges +q1 and +q2 are placed a finite distance d apart. It is desired to put a third charge q3 in between these two charges, so that q3 is in equilibrium. This is

Three infinite plane sheets carrying uniform charge densities \(-\) \(\sigma\), 2\(\sigma\), 4\(\sigma\) are placed parallel to XZ-plane at Y = a, 3a, 4a respectively. The electric field at the point (0, 2a, 0) is

A metal sphere of radius R carrying charge q is surrounded by a thick concentric metal shell of inner and outer radii a and b, respectively. The net charge on the shell is zero. The potential at the centre of the sphere, when the outer surf...

The variation of electric field along the Z-axis due to a uniformly charged circular ring of radius a in XY-plane as shown in the figure. The value of coordinate M will be

Four identical point masses, each of mass m and carrying charge + q are placed at the corners of a square of sides a on a frictionless plane surface. If the particles are released simultaneously, the kinetic energy of the system when they a...

As shown in the figure, a point charge q1 = + 1 \(\times\) 10-6 C is placed at the origin in xy-plane and another point charge q2 = + 3 \(\times\) 10-6 C is placed at the coordinate (10, 0).In that case, which of the following graph(s) ...

Two pith balls, each carrying charge + q are hung from a hook by two springs. It is found that when each charge is tripled, angle between the strings double. What was the initial angle between the strings?

A very long charged solid cylinder of radius a contains a uniform charge density p. Dielectric constant of the material of the cylinder is K. What will be the magnitude of electric field at a radial distance x (x < a) from the axis of the c...

A pair of parallel metal plates are kept with a separation d. One plate is at a potential + V and the other is at ground potential. A narrow beam of electrons enters the space between the plates with a velocity v0 and in a direction paralle...

Eleven equal point charges, all of them having a charge +Q, are placed at all the hour positions of a circular clock of radius r, except at the 10 h position. What is the electric field strength at the centre of the clock?

A negative charge is placed at the midpoint between two fixed equal positive charges, separated by a distance 2d. If the negative charge is given a small displacement x(x < < d) perpendicular to the line joining the positive charges, how th...

A point charge \(-\) q is carried from a point A to another point B on the axis of a charged ring of radius r carrying a charge + q. If the point A is at a distance \({4 \over 3}r\) from the centre of the ring and the point B is $${3 \over ...

The bob of a pendulum of mass m, suspended by an inextensible string of length L as shown in the figure carries a small charge q. An infinite horizontal plane conductor with uniform surface charge density \(\sigma\) is placed below it. What...

Two positive charges Q and 4Q are placed at points A and B respectively, where B is at a distance d units to the right of A. The total electric potential due to these charges is minimum at P on the line through A and B. What is (are) the di...

Four equal charges of value + Q are placed at any four vertices of a regular hexagon of side 'a'. By suitably choosing the vertices, what can be maximum possible magnitude of electric field at the centre of the hexagon?

Consider a region in free space bounded by the surfaces of an imaginary cube having sides of length a as shown in the figure. A charge + Q is placed at the centre O of the cube. P is such a point outside the cube that the line OP perpendicu...

A unit negative charge with mass M resides at the mid-point of the straight line of length 2a adjoining two fixed charges of magnitude +Q each. If it is given a very small displacement x(x << a) in a direction perpendicular to the straight ...

A charge of 0.8 coulomb is divided into two charges Q1 and Q2. These are kept at a separation of 30 cm. The force on Q1 is maximum when

A particle with charge Q coulomb, tied at the end of an inextensible string of length R metre, revolves in a vertical plane. At the centre of the circular trajectory, there is a fixed charge of magnitude Q coulomb. The mass of the moving ch...

A positive charge Q is situated at the centre of a cube. The electric flux through any face of the cube is (in SI units)

A charged particle of mass m1 and charge q1 is revolving in a circle of radius r. Another charged particle of charge q2 and mass m2 is situated at the centre of the circle. If the velocity and time period of the revolving particle be v and ...

Angle between an equipotential surface and electric lines of force is

A hollow metal sphere of radius R is charged with a charge Q. The electric potential and intensity inside the sphere are respectively

64 identical spheres of charge q and capacitance C each are combined to form a large sphere. The charge and capacitance of the large sphere is

4 point charges each +q is placed on the circumference of a circle of diameter 2d in such a way that they form a square. The potential at the centre is