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 1 cm, which placed with its axis making an angle of 60° with uniform electric field, experience a torque of \[6\sqrt{3} Nm\] . Calculate the potential energy of the dipole if it has charge ±2 nC.
In which orientation, a dipole placed in a uniform electric field is in (i) stable, (ii) unstable equilibrium?
An electric dipole is placed in an electric field generated by a point charge.
When an electric dipole p is placed in a uniform electric field E then at what angle the value of torque will be maximum?
Electric field on the axis of a small electric dipole at a distance r is E1 and at a distance of 2r on its perpendicular bisector, the electric field is E2. Then the ratio E2: E1 is ______.
Polar molecules are the molecules ______.
A dipole is placed in an electric field as shown. In which direction will it move?
Polar molecules are the molecules ______.
Two charges –q each are fixed separated by distance 2d. A third charge q of mass m placed at the mid-point is displaced slightly by x(x << d) perpendicular to the line joining the two fixed charged as shown in figure. Show that q will perform simple harmonic oscillation of time period.
`T = [(8pi^3 ε_0 md^3)/q^2]^(1/2)`
