If the distance between the charges of a dipole is doubled, and the magnitude of each charge is halved, the dipole moment will be:

The electric potential at a point on the axis of an electric dipole depends on the distance $r$ of the point from the dipole as

An electric dipole with a dipole moment of $8 imes 10^{-9} \, C \cdot m$ is placed in a uniform electric field of $5 imes 10^5 \, N/C$. What is the magnitude of the torque experienced by the dipole when it makes an angle of $30^\circ$ with the electric field?

An electrical charge $2 imes 10^{-8} \mathrm{C}$ is placed at the point $(1,2,4) \mathrm{m}$. At the point $(4,2,0) \mathrm{m}$, the electric

To increase the resonant frequency in series LCR

circuit,

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

Assertion (A): The potential $(V)$ at any axial point, at $2 \mathrm{~m}$ distance $(r)$ from the centre of the dipole of dipole moment vector $\vec{P}$ of magnitude, $4 imes 10^{-6} \mathrm{~C} \mathrm{m},$ is $\pm 9 imes 10^3 \mathrm{~V}.$

$ext{(Take }\frac{1}{4 \pi \epsilon_0}=9 imes 10^9 \mathrm{~SI ~units})$

Reason (R): $V= \pm \frac{2 P}{4 \pi \epsilon_0 r^2},$ where $r$ is the distance of any axial point, situated at $2 \mathrm{~m}$ from the centre of the dipole.

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

The electric potential due to a dipole at a point on its axis at a distance 'r' is V. If the distance is increased to '2r', the potential becomes:

Two points P and Q are maintained at the potentials of 10V and -4V respectively. The work done in moving 100 electrons from P to Q is

A positive charge is moved from low potential point A to a high potential point B. Then the electric potential energy

A small electric dipole is placed at origin with its axis being directed along the positive ${x}$-axis. The direction of electric field due to the dipole at a point $(1 {~m}, \sqrt 2 {~m}, 0)$ is along the:

Two equal charges $q$ of opposite sign separated by a distance $2a$ constitute an electric dipole of dipole moment $p.$ If $P$ is a point at a distance $r$ from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle $heta$ with the axis of the dipole, then the potential at $P$ is given by

$\left( {r > > 2a} \right)\left( {{\rm{Where\;}}p = 2\;qa} \right)$