An electric dipole of moment $ \vec { p } $ is placed in a uniform electric field$\vec { E }$ . Then
(i) The torque on the dipole is $\vec { p } \times \vec { E } $.
(ii) The potential energy of the system is $\vec { p } \cdot \vec { E } $.
(iii) The resultant force on the dipole is zero.
Choose the correct option.

An electric dipole of length 20 cm having $\pm3 \times { 10 }^{ -3 }$ C charge placed at 60 with respect to a uniform electric field experiences a torque of magnitude 6 N m. the potential energy of the dipole is:

An electric dipole is kept on the axis of a uniformly charged ring at distance $\frac{R}{\sqrt{2}}$ from the centre of the ring. The direction of the dipole moment is along the axis. The dipole moment is P, charge of the ring is Q & radius of the ring is R. The force on the dipole is ___________________.

Two electric dipoles of dipole moment $2 \space cm$ and $4 \space cm$ respectively are kept inside a cube of side $'a' \space m$. Total electric flux linked with the cube is (in SI units)

An electric dipole is kept in a non-uniform electric field. It experiences

An electric dipole placed with its axis in the direction of a uniform electric field experiences:

An electric dipole of moment $p$ is lying along a uniform electric field $E$. The work done in rotating the dipole by $90^{o}$ is:

An electric dipole of momentum $3 \times {10}^{-8}\ Cm$ is placed in an electric field of $6 \times {10}^{4}\ N/C$ with is axis making an angle of $30^o$ with the field . Find the torque acting on the dipole.

A neutral water molecule $ (H _2 O) $ in its vapour state has an electric dipole moment of $ 2 \times 10^{-24} C-m. $ If the molecule is placed in an electric field of $ 2 \times 10^{4} NC^{ _1} $ , the maximum torque that the field can exert on it is nearly.

A dipole is placed parallel to the electric field. If W is the work done in rotating the dipole by $60$, then the work done in rotating it by $180$ is:

Two charges of charge $-4\mu C$ and $+4\mu C$ are placed of the point $A(1, 0, 4)$ and $B(2, -1, 5)$ located in an electric field $E = 0.20\hat {i} V/ C-m$. Then, torque acting on the dipole will be

Dipole is placed parallel to the electric field. If W is the work done in rotating the dipole $60^0$, then work  done in rotating it by $180^0$ is

A magnetic dipole is placed at right angles to the direction of lines of force of magnetic induction B. If it is rotated through an angle of $180^0$, then the work done is 

In a certain region of space, electric field is along z-direction throughout. The magnitude of electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of $10^5 NC^{-1}$ per metre. What is the torque experienced by a system having a total dipole moment equal to $10^{-7}$ C-m in the negative z-direction?

For a dipole $q=2\times 10^{-6}C$ , d=0.01 m, find the maximum torque on the dipole if $E=5\times 10^{5}N/C$ :-

The work done in rotating a dipole through ${ 180 }^{ \circ  }$ from electric field direction is :

Total electric force on an electric dipole placed in an electric field of a point charge is :

Work done in turning dipole through an angle 60 is 

An electri dipole experience linear displacement and  rotational motion in _____ electric field.

An electric dipole consists of two opposite charges each of magnitude $ 1.0 \mu C $ separated by a distance of 2.0 cm. the diople is placed in an external electric field of $ 1.0 \times  10^5 N/C $ the maximum torque on the dipole is:

A dipole is placed in an electric field whose direction is fixed but its magnitude varies with distance. It is possible that the dipole experiences :

An electric dipole of moment p is kept along an electric field E. The work done in rotating it from an equilibrium position by an angle $\theta$ is :

An electric dipole is kept in the surrounding of another dipole, it experiences

What will be the magnitude of torque on an electric dipole having dipole moment of  $4 \times 10 ^ { - 9 }  { cm }$  placed in a uniform electric field of intensity of  $5 \times 10 ^ { 4 } { NC } ^ { - 1 }$  making an angle  $180 ^ { \circ }$  with the field.

An electric dipole, made up of positive and negative charges, each of $1\mu C$ and placed at a distance $2\ cm$ apart. If the dipole is placed in an electric field of $10^{5} N/C$ then the maximum torque which the field can exert on the dipole, if it is turned from a position $\theta = 0^{\circ}$ to $\theta = 180^{\circ}$ is, is

If a dipole of dipole moment $\displaystyle \vec { p } $ is placed in a uniform electric field $\displaystyle \vec { E } $, then torque acting on it is given by :

A dipole is placed parallel to the electric field. If W is the work done in rotating the dipole by 60, then work done in rotating it by 180 is

An electric dipole is placed in an electric field generated by a point charge.

An electric dipole is placed in non-uniform electric field, then it experiences

State whether True or False :

The torque acting on a dipole of momentum $\vec { p } $ in an electric field $\vec { E } $:

An electric dipole of moment $\vec { p } $ is placed normal to the lines of force of electric intensity $\vec { E } $, then work done in deflecting it through an angle of ${180}^{o}$ is:

An electric dipole of dipole moment $\vec { P } $ is placed parallel to the uniform electric field of intensity $\vec { E }$. On rotating it through ${180}^{o}$, the amount of work done is ________ .

An electric dipole kept in a uniform electric field experiences :

When an electric dipole $\vec p$ is kept in a uniform electric field $\vec E$ then for what of a value of the angle between $\vec p$ and $\vec E$, torque will be maximum:

What will be the magnitude of torque on an electric dipole having dipole moment of $4\times { 10 }^{ -9 }cm$ placed in a uniform electric field of intensity of $5\times { 10 }^{ 4 \,\,}N { C }^{ -1 }$ making an angle ${180}^{o}$ with the field.

An electric dipole  of dipole moment $\vec {p}$ is placed in uniform electric field $\vec {E}$, with $\vec {p}$ parallel to $\vec {E}$ . It is then rotated by an angle of $\theta$. The work done is

A dipole of $2 \mu C$ charges each other consists of the positive charge at the point $P(1, -1)$ and the m=negative charge is placed at the point $Q(-1,1)$ . The work done in displacing a charge of $ + 1 \mu C$ from point $A (-3,-3) $ to $B(4,4) $ is :

Two electric dipoles of moment $\rho $ and $64\rho $ are placed in opposite direction on a line at a distance of $25\ cm$. The electric field will be zero at point between the dipoles whose distance from dipole of moment $\rho $ is 

An electric dipole of moment 'p' is placed in an electric field of intensity 'E'. The dipole acquires a position such that the axis of the dipole makes an angle $\theta $ with the direction of the field. Assuming that the potential energy of the dipole to be zero when=${ 90 }^{ 0 }$, the torque and the potential energy of the dipole will respectively be

An electric dipole is placed in an electric field of a point charge then...........

Four equal positive charges each of magnitude $q$ are placed at the respective vertices of a square of side length $l$. A point charge $Q$ is placed at the centre of the square. Then

If we rotate the dipole of moment $p$ placed in an electric field $E$ from an $\theta _1$ to $\theta _2$, the work done by the external force is

An electric dipole of dipole moment $p$ is placed in a uniform electric field $E$ in stable equilibrium position. Its moment of inertia about the centroidal axis is $I$. If it is displaced slightly from its mean position find the period of small oscillations.

In a certain region of space, electric field is along the z-direction throughout. The magnitude of electric field is, however not constant but increases uniformly along the positive z-direction at the rate ${10^5}\,V/m.$ The force and the torque experienced by a system having a total dipole moment equal to ${10^{ - 7}}C - m$ in the negative z-direction is given by respectively.

 An electric dipole consist of two opposite charges each of magnitude $1\mu C$ separated by a distance of $2\,cm.$ The dipole is placed in an external field of ${10^5}{\text{N/C}}$.The maximum torque on the dipole is: