Gauss Law – Class 12 | Chapter – 1 | Physics Short Notes Series PDF for NEET & JEE

Gauss Law: Gauss law, also known as Gauss’s flux theorem, is a fundamental principle in electromagnetism that relates the distribution of electric charge to the electric field. The law states that the flux of the electric field through a closed surface is proportional to the charge enclosed within the surface.

Formula / Theorem of Gauss Law

Gauss’s law can be expressed as:

∮E.dA = Q/ε0

where:

• ∮E.dA is the flux of the electric field E through a closed surface, expressed as a surface integral.

• Q is the total charge enclosed within the surface.

• ε0 is the electric constant or the vacuum permittivity, which is a fundamental constant of nature equal to 8.85 x 10^-12 C²/(Nm²).

This theorem states that the electric flux through a closed surface is proportional to the charge enclosed within the surface, regardless of the shape or size of the surface. Gauss’s law can be used to determine the electric field due to a continuous charge distribution by choosing an appropriate closed surface, calculating the electric flux through the surface, and equating it to the charge enclosed within the surface.

Applications of Gauss Law

Gauss law has several important applications in the fields of electromagnetism and electrical engineering. Some of the most common applications of Gauss’s law are:

• Electric field near conductors: Gauss’s law can be used to calculate the electric field near the surface of a charged conductor. By choosing an appropriate closed surface, such as a sphere or cylinder, and using Gauss’s law, one can determine the electric field due to the surface charge density on the conductor.
• Capacitors: Gauss’s law can be used to determine the electric field inside a charged capacitor. By choosing a closed surface that encloses the plates of the capacitor, the electric flux through the surface can be calculated, which in turn can be used to determine the electric field between the plates.
• Electric potential: Gauss’s law can be used to determine the electric potential of a continuous charge distribution. By integrating the electric field over a path between two points, one can calculate the potential difference between those points.
• Electrostatic shielding: Gauss’s law can be used to analyze the behavior of electrostatic shielding, which is a technique used to reduce the electric field in a region by placing a conductive shield around it. Gauss’s law can be used to determine the electric field inside and outside the shield, which can be used to design effective shielding systems.

• Electromagnetic waves: Gauss’s law can be used to analyze the behavior of electromagnetic waves, such as light and radio waves. Gauss’s law is used to determine the electric field distribution of these waves, which is critical in the design of electromagnetic devices and systems.

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By Team Learning Mantras