Advertisements
Advertisements
प्रश्न
Define electric dipole moment. Is it a scalar or a vector? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.
Advertisements
उत्तर
Electric dipole moment: The strength of an electric dipole is measured by the quantity electric dipole moment. Its magnitude is equal to the product of the magnitude of either charge and the distance between the two charges.
Electric dipole moment, p = q × d
It is a vector quantity.
In vector form it is written as`vecp = qxxvecd`, where the direction of `vecd`is from negative charge to positive charge.
Electric Field of dipole at points on the equatorial plane:
The magnitudes of the electric field due to the two charges +q and −q are given by,
`E_(+q) = q/(4piε_0) 1/(r^2+a^2) ...... (1)`
`E_(-q) = q/(4piε_0) 1/(r^2+a^2) ...... (2)`
`therefore E_(+q) =E_(-q)`
The directions of E+q and E−q are as shown in the figure. The components normal to the dipole axis cancel away. The components along the dipole axis add up.
∴ Total electric field
`E = -(E_(+q) + E_(-q)) cos theta hatp`
[Negative sign shows that field is opposite to `hatp` ]
`E = -(2qa)/(4piε_0 r^3)hatP ........ (3)`
At large distances (r >> a), this reduces to
`E = -(2qa)/(4piε_0 r^3)hatP ....... (4)`
`because vecp = q xx 2veca hatp`
`because E = (-vecp)/(4piε_0 r^3)` ( r>>a )
APPEARS IN
संबंधित प्रश्न
An electric dipole of length 4 cm, when placed with its axis making an angle of 60° with a uniform electric field, experiences a torque of `4sqrt3`Nm. Calculate the potential energy of the dipole, if it has charge ±8 nC
- Define torque acting on a dipole of dipole moment \[\vec{p}\] placed in a uniform electric field \[\vec{E}\] Express it in the vector from and point out the direction along which it acts. Express it in the vector from and point out the direction along which it acts.
- What happens if the field is non-uniform?
- What would happen if the external field
\[\vec{E}\] is increasing (i) parallel to \[\vec{p}\] and (ii) anti-parallel to \[\vec{p}\]?
Two particles, carrying charges −q and +q and and of mass m each, are fixed at the ends of a light rod of length a to form a dipole. The rod is clamped at an end and is placed in a uniform electric field E with the axis of the dipole along the electric field. The rod is slightly tilted and then released. Neglecting gravity, find the time period of small oscillations.
An electric dipole consists of two opposite charges each 0.05 µC separated by 30 mm. The dipole is placed in an unifom1 external electric field of 106 NC-1. The maximum torque exerted by the field on the dipole is ______
An electric dipole is placed at an angle of 30° to a non-uniform electric field. The dipole will experience ________.
The electric potential V as a function of distance X is shown in the figure.
The graph of the magnitude of electric field intensity E as a function of X is ______.
A square surface of side l (m) in the plane of the paper. A uniform electric field E(V/m) also in the plane of the paper is limited only to the lower half of the square surface, the electric flux (in SI units) associated with the surface is ______.
The potential energy of a dipole in an external electric field is given by:
The electric potential at a point P due to a dipole (at distance r from the centre, at angle θ from the dipole axis) is given by:
Water (H₂O) exhibits a dipole moment of approximately 1.85 D. The primary reason is:
