Class 12 Physics: Electrostatics

Class 12 Physics: Electrostatics

Electrostatics is a branch of physics which studies the properties of electric charges at a stationary position. Almost all of us are fairly familiar with some of these electrostatic phenomena, such as the attraction of small pieces of paper to the comb, after you use it. The attraction of the plastic wrap to your hand after you remove it from a package and flashes coming out from your woolen sweater or blanket during the dry winter season are all examples of electrostatic phenomena. These electrostatic phenomena arise due to the forces between electric charges and the description of these forces are governed by Coulomb’s law.

Coulomb’s Law of Electrostatics

The magnitude of the electrostatic force between two point charges is directly proportional to the product of the magnitude of charges and is inversely proportional to the square of the distance between them. Suppose there are two point charges q and Q, separated by a distance r. If F be the electrostatic force between these two charges, then according to Coulomb’s law

    \[ \boxed{\vec{F}=\frac{1}{4\pi\epsilon_{0}}\frac{q_{1}q_{2}}{r^{2}}\hat{r}} \]

The proportionality constant \frac{1}{4\pi\epsilon_{0}} is known as Coulomb constant and its value is 8.9876\times10^9 N m^2 C^{-2} and the constant \epsilon_{0} is called the permittivity of free space. Please note that electrostatic force is a vector quantity and the direction of the force is determined by the sign of charges involved. The force will be repulsive when the two charges have same sign however the force between opposite charges will be attractive in nature.

Electrostatic field

Similar to a mass which creates a gravitational field around it, a charge produces an electric field (\vec{E}) or electrostatic field around it. This field exerts a force q\vec{E} on any charge (q) within its vicinity. Thus by definition, the electrostatic field at any location indicates the force that would act on a unit positive test charge if placed at that location. Therefore we define the electrostatic field at a given point as

    \[ \boxed{\vec{E}=\frac{\vec{F}}{q}}} \]

Suppose we have a point charge Q placed at a point A. In order to calculate the electric field at a point B which is \vec{r} away from Q, we have to place a test charge q at point B. From coulomb’s law, electric force on q is

    \[ \vec{F}=\frac{1}{4\pi\epsilon_{0}}\frac{Qq}{r^{2}}\hat{r} \]

Thus electrostatic field at point B is

    \[ \boxed{\vec{E}=\frac{1}{4\pi\epsilon_{0}}\frac{Q}{r^{2}}\hat{r}} \]

Electric field lines are useful to visualize the electric field at any given point. These lines start with positive charge and end on a negative charge and no two electric field lines cross each other. Electric field lines are parallel to the direction of the electric field at that point. Moreover, the density of these lines is directly proportional to the magnitude of the electric field at that given point. Please remember, these lines are purely geometrical construction and they have no physical existence.

Electrostatic potential

The electrostatic potential is a scalar quantity which defines the amount of work needed to move a unit positive charge from a reference point to a point within the field of influence. In physics, we typically choose infinity as this reference point. Although any point beyond the influence of the electric field can be used. The electrostatic potential due to a point charge Q at a distance \vec{r} is given by

    \[ \boxed{V=\frac{1}{4\pi\epsilon_{0}}\frac{Q}{r}}} \]

We can apply the superposition theorem to calculate the total electrostatic potential due to a system of charges. This is given by

    \[ \boxed{V=\frac{1}{4\pi\epsilon_0}\sum{\frac{Q_i}{r_i}}} \]

We can calculate electrostatic potential V, if we know the form of the electric field \vec{E}.

    \[ \boxed{V=-\int_{\infty}^{\vec{r}}{\vec{E}.d\vec{r}}} \]

Any surface with same electric potential at every point, is called an equipotential surface. The component of the electric field parallel to an equipotential surface is zero as the potential does not change. Thus the electric field is always perpendicular to the equipotential surface and the work done in moving a charge between two points on an equipotential surface is zero. The metal surface is an example of an equipotential surface.

Conductors, Insulators and Semiconductors:

  • Conductors are those material where electric current can flow freely. The outer electrons are almost free so that they can move freely throughout the body of the material. Metals like Fe, Cu, Ag, Al are examples of conductors.
  • Insulators are those material where electric current can not flow. Outermost electrons are so tightly bound to their respective atoms that there is no free electrons in these materials. Wood, plastic, glass are examples of insulators.
  • In Semiconductors current can flow partially. They behave like perfect insulators at very low temperature but the conductivity increases as we increase the temperature. These materials have their importance in the semiconductor industry such as the microprocessor. Si, Ge, GaAs are examples of semiconductors.

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