Redistribution of Charge between Two Capacitors

When s charged capacitor is connected across and uncharged capacitor, the redistribution of charge occurs to equalize the potential difference across each capacitor. Some energy is also wasted in the form of heat.

Suppose we have two charged capacitors C1 and C2 having charge Q1 and Q2 after disconnecting from their respective batteries having potential V1 and V2. These two capacitors are connected to each other.

If two capacitors of capacitance C1 and C2 are changed to potential V1 and V2 respectively. After disconnecting from the batteries they are assigned connected to each other with reverse polarity i.e. positive plate of capacitor connected to negative plate of other.

Force on a dielectric and E-x and V-x curve inside a capacitor

Force on a dielectric inside a capacitor

When a dielectric slab is inserted between the charged parallel plates, the slab experiences a force as shown in figure.

Force on the dielectric slab is given by

Where V = potential difference between the slabs at that instant.

Note: This force is independent of x (distance by which initially the slab inserted.)

E-x and V-x curve inside capacitor

If the distance between plates of a parallel plate capacitor is 5d. Let the positively charged plate is at x = 0 and negatively charged plate as at x = 5d. Two slabs one of the conductor and other of a dielectric of equal thickness d are inserted between the plates as shown in the figure. Electric field and Potential versus distance graph will look like: