Advertisements
Advertisements
प्रश्न
Find the resultant electric field due to an electric dipole of dipole moment, 2aq, (2a being the separation between the charges ±± q) at a point distant 'x' on its equator.
Advertisements
उत्तर
Consider a dipole consisting of two electric charges +q and −q between a small distance AB = 2a with centre O.
Now, let us find the electric field intensity at point P.
The magnitudes of the electric field at point P due to the two charges +q and −q are given by
`E_(+q) = q/(4πε_0) 1/(x^2+a^2) .....(1)`
and ` E_(-q) = q/(4πε_0) 1/(x^2+a^2) ...... (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 along PE and PF cancel away. The components along the dipole axis add up.
Therefore, the resultant electric field at point P is given as
`E = - (E_(+q) + E_(-q) cosΘ)` (The negative sign shows that the field is opposite to the dipole moment of the dipole.)
`E=(-2qa)/(4πε_0 (x^2+a^2)^(3/2)) ......(3)`
When point P lies at a large distance (x >> a) from the dipole, the above expression reduces to
`E = (-2qa)/(4πε_0 x^3 ) ....... (4)`
∴ `p =1 xx 2a`
∴ `E = (-p)/(4πε_0 x^3 )` (x >> a)
The direction of this electric field is along PR (or BA).
APPEARS IN
संबंधित प्रश्न
An electric dipole of length 4 cm, when placed with its axis making an angle of 60° with a uniform electric field, experiences a torque of `4sqrt3`Nm. Calculate the potential energy of the dipole, if it has charge ±8 nC
Depict the orientation of the dipole in (i) stable, (ii) unstable equilibrium in a uniform electric field.
- Define torque acting on a dipole of dipole moment \[\vec{p}\] placed in a uniform electric field \[\vec{E}\] Express it in the vector from and point out the direction along which it acts. Express it in the vector from and point out the direction along which it acts.
- What happens if the field is non-uniform?
- What would happen if the external field
\[\vec{E}\] is increasing (i) parallel to \[\vec{p}\] and (ii) anti-parallel to \[\vec{p}\]?
Answer the following question.
What is the unit of dipole moment?
When an electric dipole p is placed in a uniform electric field E then at what angle the value of torque will be maximum?
The ratio of the weight of a man in a stationary lift and in a lift accelerating downwards with a uniform acceleration α is 3 : 2. The acceleration of the lift is:
The region surrounding a stationary electric dipole has ______
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.
In an electric dipole, what is the locus of a point having zero potential?
