Electrostatics

Point charge $\sqrt{2} C, \sqrt{2} C$, and $-2 C$ are placed at the three vertices of a right-angled triangle in air. [as shown in the figure below]
What is the electric field at a point $P$ on the hypotenuse that is equidistant from all th...

Two charges 1 C and 2 C are placed at coordinates $(0,3)$ and $(4,3)$ respectively in an XY plane. What is the work done to put a 30 C charge at the origin of the coordinate system?

Two conducting spherical shells $A$ and $B$ of radii 4 cm and 6 cm respectively are placed with their centres 17 cm apart in air. Initially, sphere A was given a -20 nC charge while sphere B was uncharged. The spheres are then connected by ...

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $45^{\circ}$ with each other. When the system is immersed in a liquid of relative density 0.8 , the angle between the strings remains unch...

Two-point charges of equal magnitude 0.01 C and opposite in sign are separated by 0.2 mm , forming an electric dipole. The electric dipole moment of the dipole is:

A uniform electric field $E=3 \hat{i}+6 \hat{j}+\hat{k}$ passes through a closed cuboidal surface. One face of the cuboid has an area $4 m^2$ and an outward unit normal given by $\frac{2 \hat{i}+2 \hat{j}+3 \hat{k}}{\sqrt{17}}$. If the elec...

A charge of $5 \mu \mathrm{C}$ is placed at the centre of a spherical shell $S_1$ of radius 10 cm . Now this system is enclosed inside another spherical shell $S_2$ of radius 20 cm . The ratio of the electrical flux through the surface $S_2...

Bodies $P, Q, R, S$ are labelled as having charges $Q_P=0.5 \times 10^{-19} C, Q_Q=0.7 \times 10^{-19} C$, $Q_R=2.1 \times 10^{-19} C, Q_S=4.8 \times 10^{-19} C$ respectively.
Select the body having the correct charge.
[Given electronic cha...

In a uniform electric field $10^6 N C^{-1}$ an electric dipole of length 4 cm is placed with its axis making an angle $60^{\circ}$ with the electric field. If the dipole experiences a torque of $8 \sqrt{3} \mathrm{~N} \mathrm{~m}$.
Find the...

Uniform electric field of $5 \times 10^3 \mathrm{NC}^{-1}$ is maintained in the positive Y direction. Now a point charge of $2 \times 10^{-4} \mathrm{C}$ at rest is released from the origin. The kinetic energy attained by the charge when it...

A pith ball of mass ' $m$ ' gram and charge ' $Q$ ' is suspended using a mass less silk thread near a large charged conducting metal sheet of area ' $A$ ' and surface charged density ' $\sigma$ '. If the silk thread makes an angle $\Theta$ ...

Two point charges $P=+25 \mu C$ and $Q=-16 \mu C$ are placed 5 cm apart. Find the position of the point at which the resultant electric field is zero:

For the charge configuration shown here, which of the following is not true?

Point charges $-3 Q,-q, 2 q$ and $2 Q$ are placed, one at each corner of a square. The relation between Q and q for which the potential at the centre of the square is zero is

Two identical conducting balls having positive charges $q_1$ and $q_2$ are separated by a distance $r$. If they are made to touch each other and then separated to the same distance, the force between them will be

Three charges, $Q,-q$ and $2 q$ are placed at the vertices of a right-angled isosceles triangle. What is the value of $q$ for the net electrostatic energy of the configuration to be zero?

A uniformly charged conducting sphere of 0.2 m diameter has a surface charge density of $70 \mu \mathrm{Cm}^{-2}$. The electric flux leaving the surface of the sphere is:

A particle of mass 3 g and charge $60 \mu \mathrm{C}$ is released from rest in a uniform electric field of intensity $10^5 N C^{-1}$. If the value of kinetic energy attained by the particle after moving through a distance of 2 cm is $m \tim...

Two electric dipoles of dipole moments $3.9 \times 10^{-30} \mathrm{Cm}$ and $5.2 \times 10^{-30} \mathrm{Cm}$ are placed in two different uniform electric fields of strengths $16 \times 10^4 \mathrm{NC}^{-1}$ and $4 \times 10^4 \mathrm{NC}...

A bob of a simple pendulum has a mass of 4 g and a charge of $20 \mu \mathrm{C}$. If it is at rest in a uniform horizontal electric field of intensity $1000 \mathrm{Vm}^{-1}$, the angle that the pendulum makes with the vertical at equilibri...

The electric field versus distance graph is shown as given. Select the correct statement from the following.
E- electric field
R-radius
r - distance from the centre

What is the dimensional formula for electric flux?

When a metallic spherical shell of radius 20 cm is charged, the potential on its surface is found to be 5 V . The potential at a point 10 cm from the centre of the spherical shell is :

A particle ' X ' carrying a charge +Q is moving in a circular path of radius R around another particle ' Y ' having a charge -Q with a frequency ' $v$ '. Then the mass ' $m$ ' of the charged particle is

Three point charges $-1 C,+1 C,+1 C$ are placed at points $A, B, C$ respectively of a triangle $A B C$. What is the total potential energy of the system? [given $\mathrm{AB}=\mathrm{AC}=6 \mathrm{~cm}$ and $\mathrm{BC}=3 \mathrm{~cm}$ ]

Five charges, '\(q\)' each are placed at the comers of a regular pentagon of side '\(a\)' as shown in figure. First, charge from '\(A\)' is removed with other charges intact, then charge at '\(A\)' is replaced with an equal opposite charge....

Two charges '\(-q\)' each are fixed, separated by distance '\(2 d\)'. A third charge '\(q\)' of mass '\(m\)' placed at the mid-point is displaced slightly by '\(x\)' \((x< < d)\) perpendicular to the line joining the two fixed charges as sh...

A square shaped aluminium coin weighs \(0.75 \mathrm{~g}\) and its diagonal measures \(14 \mathrm{~mm}\). It has equal amounts of positive and negative charges. Suppose those equal charges were concentrated in two charges \((+Q\) and $$-Q)$...

Two metal spheres, one of radius \(\frac{R}{2}\) and the other of radius \(2 \mathrm{R}\) respectively have the same surface charge density They are brought in contact and separated. The ratio of their new surface charge densities is

If potential (in volt) in a region is expressed as \(\mathrm{V}(\mathrm{x}, \mathrm{y}, \mathrm{z})=6 \mathrm{xy}-\mathrm{y}+2 \mathrm{yz}\), the electric field (in \(N C^{-1}\)) at point \((1,0,1)\) is

Three point charges are located on a circular arc at \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) as shown in the figure below. The total electric field at the centre of the \(\operatorname{arc}(\mathrm{C})\) is

A neutral water molecule is placed in an electric field \(E=2.5 \times 10^4 \mathrm{NC}^{-1}\). The work done to rotate it by \(180^{\circ}\) is \(5 \times 10^{-25} \mathrm{~J}\). Find the approximate separation of centre of charges.

If 216 drops of the same size are charged at \(200 \mathrm{~V}\) each and they combine to form a bigger drop, the potential of the bigger drop will be

Two point charges \(\mathrm{M}\) and \(\mathrm{N}\) having charges \(+q\) and \(-q\) respectively are placed at a distance apart. Force acting between them is \(\mathrm{F}\). If \(30 \%\) of charge of \(\mathrm{N}\) is transferred to $$\mat...

3 point charges each of \(-\mathrm{q}\) are placed on the circumference of a circle of diameter \(2 \mathrm{a}\) at \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) respectively as shown in figure. The electric field at \(\mathrm{O}\) is

A uniformly charged solid sphere of radius \(\mathrm{R}\) has potential \(\mathrm{V}_0\) (measured with respect to infinity) on its surface. For this sphere the equipotential surfaces with potentials $$\frac{3 \mathrm{~V}_0}{2}, \frac{\math...

Figure shows three arrangements of electric field lines. In each arrangement, a proton is released from rest at point \(\mathrm{P}\) and then accelerated through point \(\mathrm{Q}\) by the electric field. Points \(\mathrm{P}\) and $$\mathr...

A tiny ball of mass \(\mathrm{m}\) and charge \(\mathrm{q}\) is suspended from the fixed support using an insulating string of length \(1 \mathrm{~m}\). The horizontal uniform electric field \(\mathrm{E}\) is switched on. The angle made by ...

The force between two electric point charges at rest in air is \(F_1\) When the same arrangement is kept inside water, the force between them is \(F_2\). Which of the following statement is correct?

An electron and a proton having mass \(m_e\) and \(m_p\) respectively, initially at rest, move through the same distance '\(s\)' in a uniform electric field '\(E\)'. If the time taken by them to cover that distance is \(t_e\) and \(t_p\) re...

PQRS is square of side \(1 \mathrm{~m}\). A charge of \(100 \mu \mathrm{C}\) is placed at the centre of the square. Then the work done to take \(3 \mu \mathrm{C}\) charge from the corner \(\mathrm{P}\) to the corner \(\mathrm{R}\).

A spherical metal ball of density '\(\rho\)' and radius '\(r\)' is immersed in a liquid of density '\(\sigma\)'. When an electric field is applied in the upward direction the metal ball remains just suspended in the liquid. Then the express...

Two point charges \(20 \mu \mathrm{C}\) and \(-10 \mu \mathrm{C}\) are separated by a distance of \(1 \mathrm{~m}\) in air. At what point on the line joining the two charges, the electric potential is zero.

When \(10^{19}\) electrons are removed from a neutral metal plate, the electric charge on it is

Two charged spheres of \(-20\mu\)C and \(60\mu\)C are kept at a certain distance. They are touched and kept again at the same distance. What is the ratio of force experienced before and after?

Charge on electron is

Which of the following diagram represents the variation of the electric field with distance r from the centre of a uniformly charged non-conducting sphere of radius R?

What is the electric field near infinite plane sheet of charge density \(\sigma\) ?

Work done in moving a charge of 25C is 50 J. Calculate potential difference, between two points.

Insulators can be charged by which of the following process?