Gauss’s Law
It is among the four equations of Maxwell’s laws of electromagnetism. It was initially formulated by Carl Friedrich Gauss in the year 1835 and relates the electric fields at the points on a closed surface area and the net charge enclosed by that surface. The law was released in 1867 as part of a collection of work by the popular German mathematician, Carl Friedrich Gauss.
Statement of Gauss’s Law
Gauss Law states that the net electric flux out of a closed surface area is equal to the charge enclosed divided by the permittivity. The electric flux in an area is defined as the electric field multiplied by the area of the surface projected in a plane and perpendicular to the field.
Electric Flux
The electrical flux is specified as the electrical field traveling through a given area multiplied by the area of the surface in a plane perpendicular to the field. Yet another statement of Gauss’s law states that the net flux of an offered electrical field through an offered surface, divided by the enclosed charge must be equal to a constant.
Normally, a positive electric charge is expected to generate a positive electrical field.
Gauss’s Law Mathematical Expression
According to the Gauss law, the overall flux linked with a closed surface area is 1/ ε0 times the charge confined by the closed surface.
For instance, a point charge q is positioned inside a cube of edge ‘a’. Now as per Gauss law, the flux through each face of the cube is q/6 ε0.
The electrical field is the fundamental principle to know about electrical flux. Generally, the electric field of the surface area is determined by using Coulomb’s law, but to calculate the electric field distribution in a closed surface, we need to understand the principle of Gauss law. It explains the electrical charge enclosed in a closed or the electric charge present in the enclosed closed surface.
Based on the Gauss theorem, the total charge confined in a closed surface area is proportional to the overall flux enclosed by the surface area. Therefore, if ϕ is overall flux and ϵ0 is electric constant, the total electric charge Q confined by the surface area is;
Q = ϕ ϵ0
The Gauss law formula is expressed by;
ϕ = Q/ ϵ0
Where,
- Q = overall charge within the provided surface,
- ε0 = the electrical constant.
Applications of Gauss’s Law
- Gauss’s law is extremely practical in figuring out expressions for the electrical field, even though the law is not directly about the electrical field; it is about the electrical flux.
- Gauss’s law can be used to derive Coulomb’s law and vice versa. Keep in mind that since Coulomb’s law only applies to point stationary charges, there is no factor to expect Gauss’s law to hold for moving charges based upon this derivation alone. In fact, Gauss’s law does hold for moving charges, and in this respect, Gauss’s law is more basic than Coulomb’s law.
MCQs about Gauss’s Law
- What is Gauss’s Law primarily concerned with?
- A. Magnetic fields
- B. Electric fields
- C. Gravitational fields
- D. Mechanical fields
- Answer: B
- Who formulated Gauss’s Law?
- A. Michael Faraday
- B. Isaac Newton
- C. Carl Friedrich Gauss
- D. James Clerk Maxwell
- Answer: C
- How is electric flux defined?
- A. Electric field divided by charge
- B. Charge divided by electric field
- C. Electric field multiplied by surface area
- D. Charge multiplied by surface area
- Answer: C
- What does Gauss’s Law state about the net electric flux through a closed surface?
- A. It is inversely proportional to the charge enclosed
- B. It is directly proportional to the charge enclosed
- C. It is equal to the permittivity divided by the charge enclosed
- D. It is equal to the charge enclosed multiplied by the permittivity
- Answer: B
- What is the mathematical expression of Gauss’s Law?
- A. ϕ = Q/ ε0
- B. Q = ϕ ε0
- C. ε0 = Q/ ϕ
- D. Q = ε0/ ϕ
- Answer: A
- How is the total flux related to the charge enclosed according to Gauss’s Law?
- A. Directly proportional
- B. Inversely proportional
- C. Exponentially proportional
- D. Logarithmically proportional
- Answer: A
- What is the value of the electrical constant in Gauss’s Law?
- A. 8.85 × 10^-12 C^2/N*m^2
- B. 6.67 × 10^-11 N*m^2/kg^2
- C. 9.8 m/s^2
- D. 3.00 × 10^8 m/s
- Answer: A
- How is electric flux calculated?
- A. Charge divided by area
- B. Electric field divided by area
- C. Charge multiplied by area
- D. Electric field multiplied by area
- Answer: D
- Which law can be derived from Gauss’s Law?
- A. Ohm’s Law
- B. Coulomb’s Law
- C. Ampere’s Law
- D. Faraday’s Law
- Answer: B
- What does Gauss’s Law relate to regarding a closed surface?
- A. Electric potential
- B. Magnetic field strength
- C. Net electric flux
- D. Electron density
- Answer: C
- In Gauss’s Law, what is the significance of the permittivity constant?
- A. It represents the charge enclosed within the surface
- B. It represents the electric field strength
- C. It represents the ability of a material to store charge
- D. It represents the relationship between charge and electric flux
- Answer: D
- What is the relation between Gauss’s Law and Coulomb’s Law?
- A. Gauss’s Law is derived from Coulomb’s Law
- B. Coulomb’s Law is derived from Gauss’s Law
- C. Both laws are independent of each other
- D. Gauss’s Law contradicts Coulomb’s Law
- Answer: B
- Which physicist formulated Gauss’s Law?
- A. Albert Einstein
- B. Nikola Tesla
- C. Carl Friedrich Gauss
- D. Thomas Edison
- Answer: C
- How does Gauss’s Law contribute to understanding the electric field?
- A. It directly calculates the electric field
- B. It indirectly provides expressions for the electric field
- C. It measures the charge density directly
- D. It determines the magnetic field around a conductor
- Answer: B
- What aspect of electric fields does Gauss’s Law focus on?
- A. Intensity
- B. Flux
- C. Voltage
- D. Resistance
- Answer: B
- Which quantity does Gauss’s Law relate to in terms of the enclosed surface?
- A. Electric charge
- B. Magnetic flux
- C. Temperature
- D. Velocity
- Answer: A
- How is the electric flux through a closed surface related to the charge enclosed?
- A. It is directly proportional
- B. It is inversely proportional
- C. It is exponential
- D. It is logarithmic
- Answer: A
- What is the primary concern of Gauss’s Law?
- A. Heat transfer
- B. Electric circuits
- C. Electric fields and charge distribution
- D. Mechanical motion
- Answer: C
- What is the unit of the electric constant?
- A. N/m
- B. C/N
- C. N*m^2/C^2
- D. C^2/N*m^2
- Answer: D
- How does Gauss’s Law contribute to understanding charge distribution?
- A. It provides direct measurements of charge
- B. It calculates charge density
- C. It relates charge to electric flux
- D. It measures charge flow
- Answer: C
- Which theorem can be derived from Gauss’s Law?
- A. Ampere’s Theorem
- B. Biot-Savart Theorem
- C. Coulomb’s Theorem
- D. Stokes’ Theorem
- Answer: D
- What principle does Gauss’s Law exemplify in electromagnetism?
- A. Conservation of charge
- B. Conservation of energy
- C. Conservation of momentum
- D. Conservation of flux
- Answer: A
Wrap up
Gauss’s Law, a cornerstone of electromagnetism, established by Carl Friedrich Gauss in 1835, relates electric fields to net enclosed charge within a closed surface.
The law states that the net electric flux through a closed surface is proportional to the charge enclosed, divided by the permittivity. Electric flux, defined as the electric field multiplied by the area perpendicular to the field, plays a crucial role in understanding Gauss’s Law.
Mathematically, Gauss’s Law expresses the total flux through a closed surface as 1/ε0 times the enclosed charge. This relationship is fundamental for determining electric field distributions within closed surfaces.
Applications of Gauss’s Law extend to deriving Coulomb’s Law and understanding electric field expressions. Despite focusing on electric flux rather than the field itself, Gauss’s Law provides a fundamental understanding of electromagnetism, applicable even to moving charges.
Overall, Gauss’s Law serves as a foundational principle in electromagnetism, facilitating the analysis and understanding of electric fields and charge distributions in various practical scenarios.