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प्रश्न
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 of 180°.
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उत्तर
(i) Consider an electric dipole consisting of two equal and opposite point charges, −q at A and + q at B, separated by a small distance 2a.
AB = 2a, having dipole moment
`|vecP| = q(2a)`
Let this dipole be held in a uniform external electric field `vecE`at an angle θ with the direction of `vecE`
Force on charge −q at A= − q ,`vecE` in a direction opposite to `vecE`
Force on charge +q at B = +q ,`vecE` along the direction of `vecE`
Net force on the dipole = qE − qE = 0
(ii) Work done on dipole, W = ΔU = pE (cos θ1 − cos θ2)
W = pE (cos0° − cos180°)
W = 2pE
संबंधित प्रश्न
Two charges 5 × 10−8 C and −3 × 10−8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
Derive an expression for the electric potential at any point along the axial line of an electric dipole.
An electric field of 1000 V/m is applied to an electric dipole at angle of 45°. The value of electric dipole moment is 10-29 C.m. What is the potential energy of the electric dipole?
Assertion (A): The potential (V) at any axial point, at 2 m distance (r) from the centre of the dipole of dipole moment vector `vec P` of magnitude, 4 × 10−6 cm, is ±9 × 103 V.
(Take `1/(4 pi epsilon_0)` = 9 × 109 SI units)
Reason (R): V = `+- (2 vec P)/(4 pi epsilon_0 r^2)`, where r is the distance of any axial point, situated at 2 m from the centre of the dipole.
In the light of the above statements, choose the correct answer from the options given below:
An electric dipole consists of two equal and opposite charges, +q and −q, separated by a small distance 2a. What is the magnitude of its dipole moment and in which direction is it directed?
Since \[p\cos\theta = \vec{p} \cdot \hat{r}\], the dipole potential at a point (r >> a) written in compact vector form is:
The electric potential at any point on the equatorial line of a dipole (θ = 90°) is:
In the general formula for the potential due to a dipole, setting θ = 0° and θ = 90° respectively recovers which two special cases?
A water molecule (H₂O) behaves like a natural electric dipole because:
At an axial point located on the side of the negative charge (θ = 180°), the potential due to the dipole is:
