Advertisements
Advertisements
प्रश्न
Answer the following question.
Derive an expression for the electric field due to a dipole of dipole moment `vec"p"` at a point on its perpendicular bisector.
Advertisements
उत्तर
The magnitudes of the electric field due to the two charges +q and −q are given by,
`E_(+q) = ("q")/(4πε_0) (1)/("r"^2 + a^2)` .....(i)
`E_(-q) = ("q")/(4πε_0) (1)/("r"^2 + a^2)` .....(i)
∴ `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 hat"p" ... ["negative sign shows that field is opposite to" hat"p"]`
`E = -(2qa)/(4πε_0("r"^2 + a^2)^(3/2)) hat"p"` ....(iii)
At large distances (r >> a), this reduces to
`E = -(2qa)/(4πε_0"r"^3)hat"p"` ....(iv)
∵ `vec"p" = q xx vec"2a"hat"p"`
∴ `E = (-vec"p")/(4πε_0"r"^3)` ...(r>>a).
APPEARS IN
संबंधित प्रश्न
Why do the electrostatic field lines not form closed loops?
- An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?
- Explain why two field lines never cross each other at any point?
Which among the curves shown in the fig. cannot possibly represent electrostatic field lines?
(a)
(b)
(c)
(d)
(e)
A point charge (+Q) is kept in the vicinity of an uncharged conducting plate. Sketch the electric field lines between the charge and the plate?
Draw the pattern of electric field lines, when a point charge –Q is kept near an uncharged conducting plate.
Explain why two field lines never cross each other at any point?
A point positive charge is brought near an isolated conducting sphere (figure). The electric field is best given by ______.
If Ea be the electric field strength of a short dipole at a point on its axial line and Ee that on the equatorial line at the same distance, then:
