Electric Charges And Fields

For a dipole having two charges and separated at a distance , the intensity of electric field at an axial point is given by where is dipole moment.
The direction of electric field is along the axis of the dipole from negative charge towards positive charge.

Two equal and opposite charges are placed at a distance d.Electric field at centre due to
charge
Similarly, electric field due to charge
Therefore, net electric field at point

For a thin uniformly charged spherical shell, the field points outside the shell at a distance from the centre is

If the radius of the sphere is


This is inversely proportional to square of the distance from the centre. It is as if the whole charge is concentrated at the centre.

Electric flux


units

In air the force of attraction between two charges is
In dielectric medium the force of attraction between two charges is

Thus, force decreases K-times.

For stability of equilibrium, the orientation of the dipole is .

The unit of physical quantity obtained by the line integral of electric field is

The flux passing through the square of 1 m placed in plane inside the eiectric field is zero because by Gauss theorem we can say here closed circuit not formed.

Electric lines of force and open while magnetic lines of force and closed loops.

For a infinite line charge,

Eight identical cubes are required so that the given charge appears at the centre of the bigger cube
Thus, the electric flux passing through the given cube is

Total charge o f the system,
Distance between two charges at points and ,

Electric dipole moment of the system is given by,


, along positive -axis

Three electric fields will be equal in magnitude and opposite in direction. Therefore, electric field at the centre is zero