Electric Dipoles

How much work will be done by an external agent to turn an electric dipole of moment $P$ through 

(ii) $180°$ (end-for-end) and $360°$ from the direction of the electric field ?

How much work will be done by an external agent to turn an electric dipole of moment $P$ through 

(i) $90°$ (end-for-end) and $360°$ from the direction of the electric field?

Show mathematically that the potential at a point on the equatorial line in an electric dipole is zero.

Which orientation of an electric dipole is a uniform electric field would correspond to stable equilibrium ?

Electric dipole moment is equal to the product of the magnitude of either charge of the dipole and the distance between the charges.

Write the $S.I.$ unit of 

(i) electric field intensity 

What is the energy in electron-volt of a photo-electron moving with velocity $2\times {10}^{7 }m/s$ ? Given mass of electron $=9.1\times {10}^{-28} gm$.

The distance of the field point, on the equatorial plane of a small electric dipole, is halved. By what factor will the electric field, due to the dipole change ?

Give the dependence of electrostatic potential due to a small electric dipole at a far off point lying on (i) the axial line

(ii) the equatorial line.

Give the dependence of electrostatic potential due to a small electric dipole at a far off point lying on 

(i) the axial line,

An electric dipole is formed by two charges $q$ and $-q$ placed at the two ends of an insulating rod of length $d$ and negligible mass. Write down the dipole moment. Is it a vector or a scalar?

Two electric dipoles, each of dipole moment p are placed at right angle to each other at the origin, one along the X -axis and the other along the Y -axis. Find the electric field at a distance r from the origin in a direction making an angle $\mathrm{\theta }$ with the X axis.

A freely suspended electric dipole is found to oscillate about its equilibrium position with a frequency $31.83 \mathrm{Hz}$. Find the strength of the electric field. Given : moment of the dipole is $2\times {10}^{-11} \mathrm{cm}$ and moment of inertia of the dipole about its centre of mass is $3\times {10}^{-10}{\mathrm{kgm}}^2.$ 

Find the binding energy of a dipole consisting of two charges $5\mu \mathrm{C}$ and $-5\mu \mathrm{C}$ separated by a distance $25\mu$ micron 

A dipole of moment $\overrightarrow{p}={10}^{-8}(5\hat{i}+\hat{j}-2\hat{k})\mathrm{cm}$   is placed in $\overrightarrow{E}={10}^{8(\hat{i}+\hat{j}+\hat{k})}{\mathrm{Vm}}^{-1}$. Find the torque acting on the dipole?

An electric dipole is placed at an angle of ${30}^{°}$ to a nonuniform electric field. The dipole will experience

An electric dipole of length $2 \mathrm{cm}$ is placed with its axis making an angle of $60°$ to a uniform electric field of ${10}^5 \mathrm{N}/\mathrm{C}$. If it experiences a torque of $8\sqrt{3}\mathrm{Nm}$ Calculate the magnitude of the charge on the dipole and potential energy of the dipole.

An electric dipole of length $4 \mathrm{cm},$ when placed with its axis making an angle of $60°$ with a uniform field experiences a torque of $4\sqrt{3}$Nm. Calculate the potential energy of the dipole, if the dipole has charges of $\pm 8\mathrm{nC}$

An electric dipole of length $4 \mathrm{cm},$ when placed with its axis making an angle of $60°$ with a uniform field experiences a torque of $4\sqrt{3}$$\mathrm{Nm}$ Calculate the

(i) magnitude of the electric field 

An electric dipole of moment $4\times {10}^{-10} \mathrm{cm}$ is placed in a uniform electric field of intensity $10\times {10}^6 \mathrm{V}/\mathrm{m}.$ Find its maximum and minimum potential energy.