P. P. C properties 02

Capacitor of P. P. C when a conducting slab placed between it's plates

If Co be the initial capacitance of P. P. C 

                 Co = EoA/d

Where, Eo = permittivity of medium between plates

 Suppose initially the charges on the capacitor plates are +-Q. Then the uniform electric field set up between the capacitor plates is

                   E0 = charge density of plates/Eo
Where E0 = electric field between the capacitor plates

           W. K. T

Charge density of plates = Q/A

So, it means
                      E0 = Q/AEo

 When a conducting slab of thickness t smaller then d is placed between the capacitor plates, free electrons flow inside it so as to reduce the field to zero inside the slab, charges -Q and +Q appera on the upper and lower faces of the slab. Now the electric field existed only in the vacuum regions between the plates of the capacitor on the either side of the slab, i.e. , the field exists only in thickness d-t, therefore, potential difference between the plates of the capacitor is

          V = E0(d-t) = Q(d-t) /AEo

Thus,

  Capacitance of the capacitor in the presence of conducting slab becomes

            C = Q/V = EoA/(d-t) = EoA. d/d.(d-t)

                              Or 

            C = (d/d-t)×Co

Clearly, C is greater then Co. Thus the introduction of a conducting slab of thickness t in a parallel plate capacitor increases its capacitance by a factor of d/d-t.

 Some important uses of capacitors 

1. To produce electric fields of desired patterns, e. g., for militants experiment

2. In radio circuits for tuning. 

3. In power supplies for smoothing the rectified current. 

4. For producing rotating magnetic fields in induction motors. 

5. In the tank circuit of oscillators.

                               Special case

If the conducting slab  fills the entire space between the plates, then t = d, we get 

             C = infinity