Thursday, November 22, 2012

The Field of An Electric Dipole

THE FIELD OF AN ELECTRIC DIPOLE
It is the space around the dipole in which the electric effect of the dipole can be experienced

(i)                 For points on the axis
Let the point P be at distance r from the centre of the dipole on the side of the charge q, as shown in Fig. a.

Then
Where ˆp is the unit vector along the dipole axis (from –q to q). Also

The total field at P is

ii) For points on the equatorial plane

The magnitudes of the electric fields due to the two charges +q and –q are given by

The directions of E+q and Eq are as shown in Fig. b. Clearly, the components normal to the dipole axis cancel away. The components along the dipole axis add up.
The total electric field is opposite to ˆp. We have E = – (E +q + E q ) cosθ ˆp. At large distances (r >> a), this reduces to

From Equations it is clear that the dipole field at large distances does not involve q and a separately; it depends on the product qa. This suggests the definition of dipole moment.

The dipole moment vector p of an electric dipole is defined by p = q × 2a ˆp that is, it is a vector whose magnitude is charge q times the separation 2a (between the pair of charges q, –q) and the direction is along the line from –q to q.

In terms of p, the electric field of dipole at large distances takes simple forms:

Notice the important point that the dipole field at large distances falls off not as 1/r 2 but as1/r 3. Further, the magnitude and the direction of the dipole field depend not only on the distance r but also on the angle between the position vector r and the dipole moment p.
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Some of these questions which may be asked in your Board Examination 2012-2013

Q1: what are the characteristic of charges acquired by the objects on rubbing against each other?

Q2: Who suggested first that there are two kinds of charges?

Q3: How can you show that there are two types of charges?

Q4: An ebonite rod is rubbed with the fur or wool. What type of charges do they acquire?

Q5Is mass of body affected on charging?

Q6: What is the polarity of charge?