Class 12 Physics: Electrostatics

Class 12 Physics: Electrostatics

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Last updated on September 10th, 2019 at 05:19 am

Electrostatics is a branch of physics that studies the properties of electric charges at a stationary position. Almost all of us are reasonably familiar with some of these electrostatic phenomena. Take the example of the attraction of small pieces of paper to the comb, after being used. 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 Coulomb’s law governs the description of these forces.

Coulomb’s Law of Electrostatics

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


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 sign of charges involved determines the direction of the force. The force will be repulsive when the two charges have the same sign; however, the force between opposite charges will be attractive in nature.

Electrostatic Field

Similar to a mass that 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 indicates the force that acts on a unit positive test charge, 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 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 a 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 Field Due to Different Situations

Electrostatic Potential

The electrostatic potential is a scalar quantity that 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 the 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 materials 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 materials where electric current can not flow. Outermost electrons are so tightly bound to their respective atoms that there is no free electron 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.