Electric Charges and Field


   
 
Electric Dipole
It is a pair of point charges with equal magnitude and opposite in sign separated by a distance.
 
Many physical systems from molecules to TV antenna can be described as electric dipoles. A water molecule is an example of an electric dipole. Even though the water molecule as such is neutral, the chemical bonds within the molecule causes displacement of charges. This displacement of charges creates a dipole with a negative charge on the oxygen end and a net positive charge on the hydrogen end.
 
 
If water molecules were not electric dipoles, water would have been a poor solvent.
 
The Field of an Electric Dipole
 
Electric field produced by a dipole is known as dipole field.
 
Let +q and -q be equal and opposite point charges separated by a small distance 2l. The strength of an electric dipole is measured by a vector quantity known as electric dipole moment known as electric dipole moment , which is the product of the charge and separation between the charges, that is
 
 
The direction of is always from negative to positive. The SI unit of dipole movement is Coulomb-meter.
 
(a) For points on axial line
 
The axial line of a dipole is the line passing through the positive and negative charges of the electric dipole.
 
 
Consider a system of charges (-q and +q) separated by a distance 2a. Let 'P' be any point on an axis where the field intensity is to be determined.
 
Electric field at P (EB) due to +q
 
 
Electric field at P due to -q (EA)
 
 
Net field at P is given by
 
 
 
 
Simplifying, we get
 
 
 
 
 
As a special case :
 
 
(b) For points on the equatorial line
 
An equatorial line of a dipole is the line perpendicular to the axial line and passing through a point mid way between the charges.
 
Electric Field Intensity due to a Dipole at a Point lying on the Perpendicular Bisector of a Dipole
 
 
Consider a dipole consisting of -q and +q separated by a distance 2a. Let P be a point Consider a point P on the equatorial line.
 
 
 
 
 
The resultant intensity is the vector sum of the intensities along PA and PB. EA and EB can be resolved into vertical and horizontal components. The vertical compents of EA and EB cancel each other as they are equal and oppositely directed. It is the horizontal components which add up to give the resultant field.
 
 
 
E = 2EA cos q
 
 
 
 
As 2qa = p
 
As a special case,
 
 
We find that at very far off points i.e., 2a < r.< r.
 
Electricity intensity at an axial point is twice the electric intensity on the equatorial line.
 
  
     
   
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