Home
Class 12
PHYSICS
In the figure shown, an electric dipole ...

In the figure shown, an electric dipole is placed at a distance `x` from an infinitely long rod of linear charge density `lambda`.
(`a`) Find the net force acting on the dipole ?
(`b`) What is the work done in rotating the dipole through `180^(@)` ?
(`c`) If the dipole is slightly rotated about its equilibrium position, find the time period of oscillation. Assume that the dipole is linearly restrained.

Text Solution

Verified by Experts

(`a`) The electric field at a distance `x` is
`E=(lambda)/(2piepsilon_(0)x)`
The net force on the dipole is
`F=p(dE)/(dx)=(2a)q[(-lambda)/(2piepsilon_(0)x^(2))]=(-lambdaqa)/(piepsilon_(0)x^(2))`
The negative sign indicates that the force is attractive.
(`b`) `W=DeltaU`
`U_(i)=-vecp*vecE=-pEcos0^(@)=-pE`
`U_(f)=-vecp*vecE=-pEcos180^(@)=+pE`
`W=2pE=2(2a)q(lambda)/(2piepsilon_(0)x)=(2lambdaqa)/(piepsilon_(0)x)`
(`c`) Restoring torque
`tau=-pEsintheta`
`tau=I(d^(2)theta)/(dt^(2))=(2ma^(2))(d^(2)theta)/(dt^(2))`
`:. 2ma^(2)(d^(2)theta)/(dt^(2))+[(lambdaqa)/(piepsilon_(0)x)]theta=0`
or `(d^(2)theta)/(dt^(2))+[(lambdaq)/(2piepsilon_(0)max)]theta=0`
`T=2pisqrt((2piepsilon_(0)max)/(lambdaq))=sqrt((8pi^(2)epsilon_(0)max)/(lambdaq))`
Promotional Banner

Similar Questions

Explore conceptually related problems

An electric dipole is placed at a distance x from centre O on the axis of a charged ring of R and charge Q uniformly distributed over it. (a) Find the net force acting on the dipole. (b) What is the work done in rotating the dipole through 180^@ ?

A short electric dipole is placed at a distance x from centre O on the axis of a ring of radius R and charge Q is uniformly distributed over tis. [(a) (find the net force acting on the dipole b) The work done external agent in rotating the dipole through 180^(@) would be

Net charge on an electric dipole is ………….. .

A short electric dipole is placed at a distance x from centre O on the axis of a ring of radius R and charge Q is uniformly distributed over tis. The net force acting on the dipole will be

A tiny electric dipole of dipole moment p is palced at a distance r from an infinitely long wire, with its vecp normal to the wire. If the linear charge density of the wire is lambda , the electrostatic force acting on the dipole is equal to

An electric dipole is placed in a uniform electric field. The net electric force on the dipole

A dipole with an electric moment p is located at a distance r from a along thread charge uniformly with a linear density lambda . Find the force F acting on the dipole if the vector p is oriented (a) along the thread (b) along the radius vector r (c ) at the right angles to the thread and the radius vector r.

A dipole with an electric moment p is located at a distance r from a along thread charge uniformly with a linear density lambda . Find the force F acting on the dipole if the vector p is oriented (a) along the thread (b) along the radius vector r (c ) at the right angles to the thread and the radius vector r.

An electric dipole is placed perpendicular to an infinite line of charge at same distance as shown in figure. Identify the correct statement.

An electric dipole is held in a uniform electric field. (i) Show that the net force acting on it is zero. (ii) The dipole is aligned parallel to the field. Find the work done in rotating it through the angle fo 180^(@) .