Question

Maxwell law explain ☺️☺️❤️❤️​

Answer 1

Answer:

Maxwell's equations are a set of four differential equations that form the theoretical basis for describing classical electromagnetism: Gauss's law: Electric charges produce an electric field. The electric flux across a closed surface is proportional to the charge enclosed.

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Answer 2

Ampere-Maxwell

• The Ampere-Maxwell equation relates electric currents and magnetic flux. It describes the magnetic fields that result from a transmitter wire or loop in electromagnetic surveys. For steady currents, it is key for describing the magnetometric resistivity experiment.

• Integral Equation
• The Ampere-Maxwell equation in integral form is given below:

b is the magnetic flux

e is the electric field

$(62)¶ \\ </h3><h3>∫S∇×b⋅da=∮Cb⋅dl=μ0(Ienc+ε0ddt∫Se⋅n^ da), \\ </h3><h3>where:$

• Ienc is the enclosed current

• μ0 is the magnetic permeability of free space

• ε0 is the electric permittivity of free space

• n^ is the outward pointing unit-normal

.

• The first term of the right hand side of the equation was discovered by Ampere. It shows the relationship between a current Ienc and the circulation of the magnetic field, b, around any closed contour line (See Fig. 36). Ienc refers to all currents irrespective of their physical origin.

• The second portion of the equation is Maxwell’s contribution and shows that a circulation of magnetic field is also caused by a time rate of change of electric flux. This explains how current in a simple circuit involving a battery and capacitor can flow. The term is pivotal in showing that electromagnetic energy propagates as waves.

For example

• , imagine integrating over a surface associated with a closed path such as the one showed in Fig. 37. We can define the surface to be the area of the circle, as in Fig. 36, or alternatively, as a stretched surface, as shown in Fig. 37. In the first case, the enclosed current is the flow of charges in the wire. In the second case, however, there are no charges flowing through the surface, yet the magnetic field defined on the enclosing curve, C, must be the same. This apparent discrepancy is reconciled if we take into account the displacement current, which is the time rate of change of the electric field, between the two plates. This integration is the same as if we were integrating over a flat surface with the current wire crossing it.

• The integral formulations are physically insightful and closely relate to the experiments that gave rise to them. They also play a formative role in generating boundary conditions for waves that propagate through different materials.

• When dealing with the propagation of EM waves in matter the currents Ienc are usually dealt with in terms of current densities. The integral equation above is thus written as

$(63)¶</p><p>∫S∇×b⋅da=∮Cb⋅dl=μ0(∫S(jf+∂p∂t+∇×m)⋅da+ε0ddt∫Se⋅n^ da),</p><p>where \: the \: current \: densities \: are:$

• jf is the free current caused by moving charges

• jp=∂p∂t is the polarization or bound current, where p is the electric polarization resulting from bound charges in dielectrics

• jm=∇×m is the magnetization current, that is, the currents needed to generate the magnetization m

$hope \: its \: help \: u$