Kara Sears
Gauss's law, which studies electric charge along with a surface and the topic of electric flux, was initially formulated by Carl Friedrich Gauss in 1835. However, it was first formulated by Joseph-Louis Lagrange in 1773. Gauss's law for electricity states that the electric flux across any closed surface is proportional to the net electric charge enclosed by the surface. The law also has a close mathematical similarity with a number of laws in other areas of physics, such as Gauss's law for magnetism and Gauss's law for gravity.
| Characteristics | Values |
|---|---|
| Name | Gauss's Law |
| First Formulated By | Joseph-Louis Lagrange in 1773 |
| First Formulated By | Carl Friedrich Gauss in 1835 |
| Field | Mathematics |
| Field | Physics |
| Field | Astronomy |
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What You'll Learn
Joseph-Louis Lagrange formulated the law in 1773
Joseph-Louis Lagrange was a prolific scientist who, during his twenty years in Berlin, contributed between one and two hundred papers to the Academy of Turin, the Berlin Academy, and the French Academy. In 1773, he formulated what would later be known as Gauss's Law. This was in the context of the attraction of ellipsoids.
Lagrange's formulation of Gauss's Law was published in his memoirs of the Turin Society in 1762 and 1773. He also published several papers in the years leading up to 1773, including a paper on the Jovian system in 1766, an essay on the problem of three bodies in 1772, and a discussion of representations of integers using quadratic forms in 1769.
In the same year that he formulated Gauss's Law, Lagrange also considered a functional determinant of order 3, a special case of a Jacobian. He also proved the expression for the volume of a tetrahedron with one of its vertices at the origin as one-sixth of the absolute value of the determinant formed by the coordinates of the other three vertices.
Following Lagrange's formulation of the law in 1773, Carl Friedrich Gauss formulated it again in 1813 or 1835. It is worth noting that the law is named after Gauss despite Lagrange's priority in its discovery.
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Carl Friedrich Gauss formulated the law in 1835
Carl Friedrich Gauss was a German mathematician, astronomer, geodesist, and physicist who contributed to many fields in mathematics and science. In 1835, he formulated Gauss's Law, which relates an electric field to the distribution of electric charges that cause it.
Gauss's Law, in its integral form, states that the flux of the electric field out of an arbitrary closed surface is proportional to the electric charge enclosed by the surface, irrespective of how that charge is distributed. This law was formulated in the context of the attraction of ellipsoids. It is one of Maxwell's equations, which forms the basis of classical electrodynamics.
Gauss's main theoretical interests in electromagnetism were reflected in his attempts to formulate quantitative laws governing electromagnetic induction. In his notebooks from these years, he recorded several innovative formulations, including the discovery of the vector potential function. In January 1835, he wrote down an "induction law" equivalent to Faraday's law, which stated that the electromotive force at a given point in space is equal to the instantaneous rate of change of this function with respect to time.
Gauss's Law makes it possible to find the distribution of electric charge. By integrating the electric field to find the flux through a small box with sides perpendicular to the conductor's surface, the charge in any given region of the conductor can be deduced. This law also has a close mathematical similarity with a number of laws in other areas of physics, such as Gauss's law for magnetism and Gauss's law for gravity.
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Gauss's Law is one of Maxwell's equations
Gauss's Law is indeed one of Maxwell's equations. It is one of four fundamental equations that describe the behaviour of electromagnetic radiation. The equations are named after the physicist and mathematician James Clerk Maxwell, who, in 1861 and 1862, published an early form of the equations that included the Lorentz force law.
Maxwell's equations are a set of partial differential equations that, along with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric and magnetic circuits. They describe how electric and magnetic fields are generated by charges, currents, and changes in the fields.
Gauss's Law, specifically, describes the relationship between an electric field and electric charges. It states that the net flux of an electric field in a closed surface is directly proportional to the enclosed electric charge. This law was first formulated by Joseph-Louis Lagrange in 1773 and later by Carl Friedrich Gauss in 1835, in the context of the attraction of ellipsoids.
Gauss's Law has a close mathematical similarity with laws in other areas of physics, such as Gauss's Law for magnetism and gravity. It can be expressed mathematically using vector calculus in integral and differential forms, which are equivalent due to the divergence theorem.
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Gauss's Law is similar to other laws in physics
Gauss's law, also known as Gauss's flux theorem or Gauss's theorem, is one of Maxwell's equations and forms the basis of classical electrodynamics. It relates the distribution of electric charge to the resulting electric field. Gauss's law can be used to derive Coulomb's law, and vice versa.
Gauss's law makes it possible to find the distribution of electric charge. It states that the total flux of an electric field in a closed surface is directly proportional to the enclosed electric charge. The law also has applications in other areas of physics, such as in the study of electric fields due to infinite wire.
The integral form of Gauss's law for gravity states that the flux (surface integral) of the gravitational field over any closed surface is proportional to the mass enclosed. This is mathematically similar to Gauss's law for electrostatics, where the flux of the electric field out of a closed surface is proportional to the electric charge enclosed.
In summary, Gauss's law is a fundamental concept in physics that has applications in various areas, including electromagnetism, gravity, and magnetism. Its similarity to other laws in physics, such as Coulomb's law and Newton's law, underscores its importance and versatility in understanding the natural world.
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Gauss's Law can be expressed mathematically in integral and differential form
Gauss's law was formulated in the context of the attraction of ellipsoids by Joseph-Louis Lagrange in 1773, followed by Carl Friedrich Gauss in 1835. Gauss's law for electricity states that the electric flux across any closed surface is proportional to the net electric charge enclosed by the surface. Gauss's law can be expressed mathematically in integral and differential form.
In its integral form, Gauss's law states that the flux of the electric field out of an arbitrary closed surface is proportional to the electric charge enclosed by the surface, irrespective of how that charge is distributed. The integral form can be expressed as:
> Φ=∫E⋅dA
Where Φ is the electric flux, E is the electric field, and dA is a vector representing an infinitesimal element of the surface.
The differential form of Gauss's law, on the other hand, is used when there is no symmetry in the problem. It states that the divergence of the electric field is proportional to the local density of charge. The differential form can be written as:
> ∇ · E = ρ/ε0
Where ∇ · E is the divergence of the electric field, ε0 is the vacuum permittivity, and ρ is the total volume charge density.
Both the integral and differential forms of Gauss's law are mathematically equivalent, as they are related by the divergence theorem, also known as Gauss's theorem. Gauss's law has close mathematical similarities with laws in other areas of physics, such as Gauss's law for magnetism and gravity.
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Frequently asked questions
Gauss's Law was first formulated by Joseph-Louis Lagrange in 1773, followed by Carl Friedrich Gauss in 1835.
Gauss's Law studies electric charge along with a surface and the topic of electric flux.
The formula for Gauss's Law in integral form is Φ=∫E⋅dA.
Coulomb's Law is a law of physics discovered experimentally by Coulomb in 1785. Gauss's Law is a mathematical theorem that applies to vector fields.
Gauss's Law can be used to find the distribution of electric charge on a conductor by integrating the electric field to find the flux through a small box perpendicular to the conductor's surface.
