Advertisements
Advertisements
प्रश्न
Answer the following question.
Derive an expression for the electric field at any point on the equatorial line of an electric dipole.
Advertisements
उत्तर
Electric field for points on the equator plane
The magnitude of the electric field due to two charges +q and –q is
`E_(+q) = q/(4piε_0)1/(r^2 + a^2)`
`E_(-q) = q/(4piε_0)1/(r^2 + a^2)`
`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)) costheta hatp` ......(Negative sign shows that the field is opposite to `hatp`)
`E = -(2qa)/(4piε_0(r^2 + a^2)^(3/2))hatp` ...(iii)
At large distance (r >> a), this reduces to,
`E = -(2qa)/(4piε_0r^3)hatp`
`vecp = q xx 2vecahatp`
`E = -vecp/(4piε_0r^3)` ....(r >> a)
संबंधित प्रश्न
An electric dipole of dipole moment`vecp` consists of point charges +q and −q separated by a distance 2a apart. Deduce the expression for the electric field `vecE` due to the dipole at a distance x from the centre of the dipole on its axial line in terms of the dipole moment `vecp`. Hence show that in the limit x>> a, `vecE->2vecp"/"(4piepsilon_0x^3)`
Write the expression for the torque \[\vec{\tau}\] acting on a dipole of dipole moment \[\vec{p}\] placed in an electric field \[\vec{E}\].
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.
Define dipole moment of an electric dipole. Is it a scalar or a vector?
On the axis and on the equator of an electric dipole for all points ____________.
A short electric dipole bas a dipole moment of 16 x 10-9 C m. The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of 60° with the dipole axis is: ____________. `(1/(4piepsilon_0) = 9 xx 10^9 "Nm"^2// "C"^2)`
In a non-uniform electric field, electric dipole experiences:-
The electric field in a region is given by `vec"E" = 2/5"E"_0hat"i"+3/5"E"_0hat"j"` with `"E"_0 = 4.0xx10^3 "N"/"C"`. The flux of this field through a rectangular surface area 0.4 m2 parallel to the Y - Z plane is ______ Nm2C-1.
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 ______.
