Gaussian s theorem for electromagnetic fields, Gaussian theorem expressions for magnetic fields

Since the magnetic field lines are closed curves, the magnetic field lines that pass through a closed surface s somewhere must be closed from there.

Another part of the surface is pierced. So, the net magnetic flux through an arbitrarily closed surface s in a magnetic field is always equal to zero, ie.

It is the magnetic Gaussian theorem, which is a fundamental law of the electromagnetic field.

Comparing Gauss's theorem with magnetic Gaussian theorem for electrostatic fields:

The principle difference between the two is that the electric field lines are emitted by electric charges, total.

It is the source that starts with a positive charge and ends with a negative charge, therefore, the electrostatic field is there.

source field; The magnetic field lines, on the other hand, are closed curves that surround the current, without a head or tail.

lines, therefore, the magnetic field is a passive field. There are discrete positive and negative "magnetic charges" (magnetic monopoles) that do not correspond to positive and negative charges in magnetic fields.

sub). The example shows that in a space where the magnetic field lines are parallel straight lines, the magnetic induction intensity values at each point on the same magnetic field line are equal.

Proof: As shown in the figure on the right, it is obtained from the magnetic Gaussian theorem.

Therefore, it is proof. t

The mathematical formula for the high-speed finger theorem is: f·ds= (f)dv.

In electrostatics, the relationship between the sum of the charges in a closed surface and the integral of the electric flux generated in that closed surface is indicated. Gauss's Law (Gauss'law) indicates the relationship between the charge distribution within the closed surface and the electric field generated.

Electrostatic and Magnetic Fields:

The two have an intrinsic regional dispersion of the family. In the electrostatic field, since there are independent charges in nature, the electric field lines have a beginning and an end point, as long as there is a net residual positive (or negative) charge in the closed surface, the electric flux through the closed surface is not equal to zero, that is, the electrostatic field is an active field.

In the magnetic field, since there is no magnetic monopole in nature, the n pole and the s pole cannot be separated, and the magnetic inductance lines are closed lines without head and tail, so the magnetic flux through any closed surface must be equal to zero.

Gauss's theorem for electrostatic fields means that the electric flux through a closed surface is only proportional to the algebraic sum of the free charges within the closed surface.

This theorem reflects that the electrostatic field is active, and the free charge is the source of the magnetic field.

It also reflects that the electric field lines are not closed, it starts from the positive charge and ends off with the negative charge.

It is important to note that although the flux depends only on the free charge inside the closed surface, the field strength on the closed surface is determined by both the internal charge and the external charge. When different charges are placed on the outside, the field strength on the closed surface will change differently, but the current flux of the closed surface will not change, as long as the internal charge does not change.

Gauss's theorem is very convenient for finding the strength of the electric field generated by a purely distributed charge.

Gauss's theorem is derived directly from Coulomb's law, which is entirely dependent on the inverse quadratic law of the forces acting between charges. Applying Gauss's theorem to a metal conductor under electrostatic equilibrium conditions, it is concluded that there is no net charge inside the conductor, so determining whether there is a net charge inside the conductor is an important method to test Coulomb's law.

In a magnetic field, since the magnetic induction line generated by the current-carrying wire is a closed line with no beginning and no end, the magnetic induction line that passes through one part of the closed curve plane s must pass through the other place, so that the magnetic flux through any closed surface s S is always equal to 0.

Magnetic fieldGauss's theoremSuitable for alternating magnetic fields.

Gauss's law. Indicates the relationship between the charge distribution within the closed surface and the electric field generated. Gauss's law is analogous to Ampère's law applied to magnetic fields in the case of electrostatic fields, and both are concentrated in Maxwell's equations.

Middle. Because of the mathematical similarity, Gauss's law can also be applied to other physical quantities determined by the inverse square law.

For example, gravity or irradiance.

Magnetic field. It is not composed of atoms or molecules, but the magnetic field is objective. The magnetic field has the radiative properties of wave particles.

There is a magnetic field around the magnet, and the phase interaction between the magnets is mediated by the magnetic field, so the two magnets can interact without physical contact. An electric current, a moving charge, a magnet, or a special form of matter that exists in the space around the changing electric field. Since the magnetism of a magnet is the same as the current, and the current is the movement of the electric charge, it is generally said that the magnetic field is generated by the change of the moving charge or electric field.