Electric Flux Density due to a Point Charge Q

   due to a Point Charge Q

AU : Dec.-03, May-06

• Consider a point charge + Q placed at the centre of the imaginary sphere of radius r. This is shown in the Fig. 3.4.1.

• The flux lines originating from the point charge + Q are directed radially outwards. The magnitude of the flux density at any point on the surface is,

• The unit vector  directed radially outwards and normal to the surface at any point on the sphere is 

• Thus in the vector form, electric flux density at a point which is at a distance of r, from the point charge + Q is given by,

1. Relationship between 

• In the last chapter, it has been derived that the electric field intensity   at a distance of r, from a point charge + Q is given by,

• Dividing the equations of due to a point charge + Q we get,

• Thus  are related through the permittivity. If the medium in which charge is located is other than free space having relative permittivity Ɛr then,

The following are the important observations :

1. The  , both act in the same direction.

2. The  are related through the permittivity of the medium in which the charge is located.

3. Though the relationship is derived considering a point charge, the result is equally applicable for any general charge distribution.

4. The electric field   due to any charge configuration is a function of the permittivity Ɛ while the electric flux density  is not.

• The relationship is very advantageous while solving the problems on multiple dielectrics.

Review Question

1. Obtain  due to a point charge Q placed at origin. Hence obtain the relation between .

AU : Dec.-03, May-06, Marks 4