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 \[\vec{p}\]?
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 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.
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 axis of the dipole 1.0 cm away from the centre.
In an electric dipole, at which point is the electric potential zero ?
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)`
