Mechanical force on charged conductor
Charge on surface of conductor
For a conductor with uniform charge distribution its surface charge density is given by
The electric field on a conductor just outside the surface is
The electric field inside the charged conductor is zero
Now we will take a charged conductor
To understand the concept of mechanical force on charged conductor we shall take a conductor with uniform charge distribution on its surface
Charge on the conductor is Q and its total surface area is S thus σ=Q/S
Electric field intensity at point A is σ/kƐo
And the Electric Field Intensity at B is zero as charge inside is zero
Now if we remove a small area say dS from the surface
There will some electric field at point A and point B due the small area ds as well as the remaining
The electric field at A and B are due to dS and due the remaining part
At the point A the net Electric field would be the sum of these fields as both of them are in same direction
But the electric field outside the charged conductor should be σ/kƐo
Similarly inside the conductor the electric field due dS and remaining is in opposite direction
But the net electric field should be zero inside the conductor, so the electric fields are equal
Therefore we obtain the final result as above
We know electric field on dS is the force exerted for unit charge of dS
Now that we know the net force we define a term force per unit area
We can replace σ / k.Ɛo with E in the above formula
Revision
For a conductor with uniform charge distribution its surface charge density is given by
The electric field on a conductor just outside the surface is
The electric field inside the charged conductor is zero
And here we get the relation for the net force
The End