Electrostatic dipole:

Electrostatic dipole consists of a pair of equal and opposite point charges separated by a very small distance. Example: H_{2}O, NH_{3} etc.

Â Electrostatic dipole moment of an electric dipole is defined as the product of the magnitude of either charge of the dipole and the dipole length. If +q and â€“q are the two charges are separated by distance 2l then dipole moment Â = q2l and the direction is from â€“q charge to +q charge. SI unit is Cm and dimension is [LTA].

Electric field intensity at a point on the axis of a dipole:

Let us consider an electric dipole consists of -q and +q at points A and B respectively separated by a distance 2a. O is the midpoint of the dipole and the dipole moment is = q2a. To calculate electric field at a point P on the axis of the dipole, at a distance r from O we consider a unit + ve test charge is placed at P.

The electric field intensity at point P due to â€“q charge is E_{1} = = Â direction is .

The electric fieldÂ intensity at point P due to +q charge is E_{2} = = direction is .

If E is the resultant electric field intensity at point P, then E = E_{2} â€“ E_{1} (direction is )

E = –

Or, E = kq[]

Or, E = Â

E =

Where k = so, E =

If r>>2a then, Â = Â .

Electric field intensity at a point on the equatorial line of a dipole: Â

Let us consider an electric dipole consists of -q and +q at points A and B respectively separated by a distance 2a. O is the midpoint of the dipole and the dipole moment is = q2a. To calculate electric field at a point P on the equatorial line of the dipole, at a distance r from O we consider a unit + ve test charge placed at P.

The electric field intensity at point P due to â€“q charge is E_{1} = Â = Â direction is .

The electric field intensity at point P due to +q charge is E_{2} = = Â direction is .

So, E_{1} = E_{2} =

The components of _{} and _{} along the equatorial line are respectively E_{1}Â and E_{2}Â cancelled due to equal in magnitude and opposite in direction. The components of _{} and _{}Â perpendicular to the equatorial line are respectively E_{1}_{Â }and E_{2}Â provide the net electric field E at point P.

E = E_{1}cosÎ¸ + E_{2}cosÎ¸Â

Or, E =

Or, E =

E =

Where k = so, E =

If r >>2a then, = .Â Â

Torque acting due to a dipole placed in uniform electric field:

Let us consider an electric dipole consists of -q and +q charge at points A and B respectively separated by a distance a is placed in the electric field of intensity E at an angle Î¸.Â The dipole moment is = qa.

Force acting on charge â€“q at A is = – and the force acting on charge +q at B is = . Since forces _{} and _{} are equal and oppositely directed, they form a couple.

The magnitude of moment of the couple i.e. torque () is given by,

= magnitude of either force Â arm of the couple

= qE BC = qE asinÎ¸ = qaEsinÎ¸ = pEsinÎ¸

Â = .

Concept of dipole moment:

Three charges +q, +q, and -2q are placed at the vertices of an isosceles triangle where the lines joining -2q with +q and +q respectively create angle Î¸. What is the dipole moment of the system?

One â€“q and one +q charge form one dipole with dipole moment P (= ql where l is the distance between â€“q and + q).

Similarly, another â€“q and +q charge form one dipole with dipole moment P.

So, the net dipole moment P^{/} =

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