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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.
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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 )
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संबंधित प्रश्न
An electric dipole is placed at the centre of a sphere. Mark the correct options.
(a) The flux of the electric field through the sphere is zero.
(b) The electric field is zero at every point of the sphere.
(c) The electric field is not zero anywhere on the sphere.
(d) The electric field is zero on a circle on the sphere.
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Two particles A and B, of opposite charges 2.0 × 10−6 C and −2.0 × 10−6 C, are placed at a separation of 1.0 cm. Calculate the electric field at a point on the perpendicular bisector of the dipole and 1.0 m away from the centre.
In an electric dipole, at which point is the electric potential zero ?
The unit of electric dipole moment is ______.
Electric dipole consists of two charges of magnitude 0.1 µC separated by a distance of 2 cm. The dipole is in 5 an external field of 105 N/C. What maximum torque does the field exert on the dipole?
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Show that intensity of electric field at a point in broadside position of an electric dipole is given by:
E = `(1/(4 pi epsilon_0)) p/((r^2 + l^2)^(3//2))`
Where the terms have their usual meaning.
