Electrostatic Potential And Capacitance

Here = 1000 R = 10
Capacitance of large drop = C

Here

According to question
= constant and therefore

We know energy per unit volume stored in electric field
in parallel plate capacitor
Energy density
Energy volume

We know

Suppose we have identical drops each having radius , capacitance , charge and potential .
If these drops are combined to form a big drop of radius , capacitance , charge and potential will become :
Charge on big drop
Capacitance of big drop
Hence potential of big drop

Capacitor increases so charge flows from the battery.

Here

The situation is as shown in the figure.

Let two equal charges Q each placed at points A and B at a distance r apart. C is the centre of AB where charge q is placed.
For equilibrium, net force on charge Q = 0


or or

Equivalent circuit becomes

Potential of a charged sphere is given by the formula

Hence, by ,

As per given information,
After splitting,


Thus, capacitance of each small drop is

Answer (d)

Normal to the conductor

Let the distance of man from each cliff be .
Thus time taken by sound to hit a cliff and return

Thus distance between the cliffs

The sphere will retain the charge for longer time, because in case of spherical metal conductor, the charge quickly spreads uniformly over the entire surface.

The given arrangement of nine plates is equivalent to the parallel combination of 8 capacitors. The capacity of each capacitor,


Hence, the capacity of 8 capacitors

Time period of simple pendulum in air


When it is suspended between vertical plates of a charged parallel plate capacitor, then accelertion due to electric field,

This acceleration is acting horizontally and acceleration due to gravity is acting vertically. So, effective acceleration

Hence,

Potential
Intensity of the electric field,

The potential of smaller sphere is given by

The potential of bigger sphere is given by

So, the potential difference between the plates

or

Here,

After separation charge is constant.
Capacity,
Capacitance decreases with increase in distance and
Potential increases with decrease in capacitance (C).

Inside the spherical shell potential is same


i.e.

From the figure, it is clear that two capacitances will from the equivalent arrangement as shown in figure

Let be the capacitance of each capacitor.
The net capacitance of and connected in parallel

Now, and are in series.


The capacitance of parallel plate capacitor

Electric potential due to point charge is given by the formula

As, all the points on equipotential surface will be equidistance from the charge.
Hence, it is spherical symmetry.

The two capacitors attain common potential given by the relation.

The final charges on two capacitors are