Advertisements
Advertisements
Question
Drive the expression for electric field at a point on the equatorial line of an electric dipole.
Advertisements
Solution
Electric Field for 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/(4piepsilon_0)1/(r^2+a^2)` .....(i)
`E_(-q)=q/(4piepsilon_0)1/(r^2-a^2)` .....(ii)
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)/(4piepsilon_0(r^2+a^2)^(3/2))hatp` .....(iii)
At large distances (r >> a), this reduces to
`E=-(2qa)/(4piepsilon_0(r^3))hatp` .....(iv)
`because vecp=qxxvec(2a)hatp`
`therefore E=(-vecp)/(4piepsilon_0(r^3))` (r >> a)
APPEARS IN
RELATED QUESTIONS
Derive the expression for the electric potential due to an electric dipole at a point on its axial line.
Define dipole moment of an electric dipole. Is it a scalar or a vector?
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. 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.
A metal sphere of radius 1 cm is given a charge of 3.14 µC. Find the electric intensity at a distance of 1 m from the centre of sphere.
`[epsilon_0 = 8.85 xx 10^-12 "F"//m]`
The electric field at a point on the equatorial plane at a distance r from the centre of a dipole having dipole moment `vec "p"` is given by, (r >> separation of two charges forming the dipole, `epsilon_0 - ` permittivity of free space) ____________.
An electric dipole of moment p is placed parallel to the uniform electric field. The amount of work done in rotating the dipole by 90° is ____________.
A dipole is placed in an electric field as shown. In which direction will it move?
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)`
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.
