Application of Gauss's law: Overview, Questions, Preparation

Following are some applications of Gauss's Law.

• Consider a charged ring of radius R on its axis at a distance x from the centre of the ring, then E = (1/4 πε₀)[qx/(R²+x²)^3/2
  
• The intensity of the electric field near a plane sheet of charge is given by E = σ/2ε₀K. Here σ is the Surface charge density.
• The field between two parallel plates of a condenser is given by E = σ/ε₀, while σ is the surface charge density.

• Charged Spheres and Shells: Gauss's Law is useful while dealing with charged spheres and spherical shells. For instance, if we have a uniformly charged sphere, we can use a Gaussian surface (an imaginary surface) that matches the sphere's symmetry to calculate the electric field at a point outside the sphere. This simplifies the calculation considerably compared to using Coulomb's law directly.
• Flux and Charge Enclosed: Gauss's Law states that the electric flux through a closed surface is directly proportional to the net charge enclosed within that surface. We can use this relationship for determining the charge inside a closed surface even if we cannot directly observe it.
• Uniformly Charged Infinite Plane: Gauss's Law helps to simplify the calculation of the electric field due to an infinite plane with uniform charge density. By using a Gaussian surface parallel to the plane, we can show that the electric field is constant and perpendicular to the plane.
• Electric Field of a Dipole: Gauss's Law can be applied to calculate the electric field of an electric dipole. By considering a Gaussian surface that encloses both the positive and negative charges of the dipole, one can show that the electric field due to a dipole falls off as the cube of the distance, which is an important concept in understanding electric field behavior.
• Closed Surfaces and Flux: Knowing the concept of closed surfaces is important while applying Gauss's Law. The total electric flux through a closed surface (Gaussian surface) depends on the total charge enclosed within that surface. This connection is useful in understanding the relationship between electric fields and charges.
• Electric Field due to Charged Rods: We can apply Gauss's Law to determine the electric field due to a uniformly charged rod. By choosing a Gaussian cylinder around the rod, we can derive the electric field at various distances from the rod.

In conclusion, Gauss's Law and its applications is a topic of great importance for the Class 12 students who are preparing for various board exams JEE, NEET, and other entrance exams.