Click for more details : Electric potential and potential energy

Equipotential Surfaces:

An equipotential surface is a surface with a constant value of potential at all points on the surface.

Properties of equipotential surfaces:

<!--[if !supportLists]-->1.     <!--[endif]-->No work is done in moving a test charge over an equipotential surfaces.

<!--[if !supportLists]-->2.     <!--[endif]-->Electric field is always normal to the equipotential surface at every point:

If the field were not normal to the equipotential surface, it would have non-zero component along the surface. To move a unit test charge against the direction of the component of the field, work would have  to be done. But this is in contradiction to the definition of an equipotential surface: there is no potential difference between any two points on the surface and no work is required to move a test charge on the surface. The electric field must, therefore, be normal to the equipotential surface at every point.

<!--[if !supportLists]-->3.     <!--[endif]-->Equipotential surfaces are closer together in the regions of strong field and farther apart in the regions of weak filed.

<!--[if !supportLists]-->4.     <!--[endif]-->No to equipotential surfaces can intersect each other.

Equipotential surfaces for different charge system: Animation

Relation between field and potential

The electric field at any point is equal to the negative of the potential gradient at that point. The negative sign shows that the direction of the electric field is in the direction of decreasing potential.

6)    <!--[endif]-->Electrostatic shielding

Consider a conductor with a cavity, with no charges inside the cavity, the electric field inside the cavity is zero, whatever be the size and shape of the cavity and whatever be the charge on the conductor and the external fields in which it might be placed. This is known as electrostatic shielding. The effect can be made use of in protecting sensitive instruments from outside electrical influence.

Dielectrics and Polarisation:

Dielectrics are non-conducting substances. In contrast to conductors, they have no (or negligible number of) charge carriers. The molecules of a dielectric substance may be polar or non-polar.

In a non-polar molecule, the centres of positive and negative charges coincide. The molecule then has no permanent (or intrinsic) dipole moment. Examples of non-polar molecules are oxygen (O₂) and hydrogen (H₂) molecules which, because of their symmetry, have no dipole moment.

On the other hand, a polar molecule is one in which the centres of positive and negative charges are separated (even when there is no external field). Such molecules have a permanent dipole moment. An ionic molecule such as HCl or a molecule of water (H₂O) are examples of polar molecules.

Polarisation:  The alignment of dipole moments of the permanent or induced dipoles in the direction of the applied electric field is called polarization.

Note: The proportionality between Q and V is true only until V becomes so large that dielectric breakdown occurs and a current then actually flows from one plate to the other through the dielectric. If dielectric breakdown occurs, the cpacitors no longer behaves like a perfect one. So, it is important to keep V below the breakdown potential for the capacitors.

Effect of Dielectric on Capacitance: Animation

If the space between the plates is filled with a medium of dielectric constant K, then the capacity C ( considering capacitance

with vacuum as C_o) will increases and  is given by

Combination of Capacitors:

Combination of n capacitors in series : Capacitors are said to be connected in series between two points if it is possible to proceed from one point to the other point along only one path.

 In the series combination, charges on the two plates (±Q) are the same on each capacitor. The total potential drop V across the combination is the sum of the resulting potential differences across each capacitor.

For ‘n’ capacitors arrangedin series

Energy Stored in A Capacitor:

The energy of a charged capacitor is measured by the total work done in charging the capacitor to a given potential.

Let assume that initially both the plates are uncharged. Now, we have to repeatedly remove small positive charges from one plate and transfer them to the other plate. At a certain stage during this process, let q be the total quantity of charge transferred.  Let v be the potential difference between the plates.

so, q= Cv

Now, when additional small charge dq is tranferred from the negative plate to the positive plate, the small amount of work done is given by

Van De Graaff Generator: It is also known as belt generator, designed in 1931 by R J Van de Graaff. This is a machine that can build up high voltages of the order of a few million volts. The resulting large electric fields are used to accelerate charged particles (electrons, protons, ions) to high energies needed for experiments to probe the small scale structure of matter.

Principle: The working of the Van de Graaff generator is based on the discharging action of points and collecting action of hollow conductor. In other words, if a charged conductor is brought in electrical contact with a hollow conductor, the charge is transferred to the hollow conductor, not matter what is the potential of the hollow conductor.

More about Van de Grraff Genertaor

Working of Van de Grraff Generator - Video 1, Video 2

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