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