Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
A short electric dipole (which consists of two point charges, +q and -q) is placed at the centre 0 and inside a large cube (ABCDEFGH) of length L, as shown in Figure 1. The electric flux, emanating through the cube is:
a) `q"/"4piin_9L`
b) zero
c) `q"/"2piin_0L`
d) `q"/"3piin_0L`
Define dipole moment of an electric dipole. Is it a scalar or a vector?
Two particles, carrying charges −q and +q and and of mass m each, are fixed at the ends of a light rod of length a to form a dipole. The rod is clamped at an end and is placed in a uniform electric field E with the axis of the dipole along the electric field. The rod is slightly tilted and then released. Neglecting gravity, find the time period of small oscillations.
When an electric dipole p is placed in a uniform electric field E then at what angle the value of torque will be maximum?
On the axis and on the equator of an electric dipole for all points ____________.
An electric dipole of moment `vec"p"` is placed normal to the lines of force of electric intensity `vec"E"`, then the work done in deflecting it through an angle of 180° is:
Polar molecules are the molecules ______.
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 ______.
Eight dipoles of charges of magnitude e each are placed inside a cube. The total electric flux coming out of the cube will be ______.
