磁学: 基础知识外文翻译资料

Wherever you go. Whatever you do. Make sure you don#39;t try to build something that doesn#39;t agree with these little gems.

Maxwell#39;s Equations

I

Gauss#39;s Law for Electricity. The surface integral of electric field over any closed surface is proportional to the enclosed charge. The k factor is the dielectric constant, equal to 1 in free space.

II

Gauss#39;s Law for Magnetism. The integral of magnetic flux density over any closed surface is zero. This is the mathematical expression of the fact that no magnetic monopoles have ever been discovered.

III

Faraday#39;s Law of Induction. The line integral of electric field over any closed path is proportional to the rate of change of magnetic flux in the enclosed region.

IV

Ampere#39;s Law (as extended by Maxwell). The line integral of magnetic flux density over any closed path is proportional to the rate of change of electric field and electric current in the enclosed region. The k_m factor is the relative permeability, equal to 1 in free space.

Those Little Constants

All of the preceding equations work with units of meters, seconds, teslas (units of induced magnetic flux density, commonly referred to as 'magnetic field' or 'field'), webers (units of induced magnetic flux), amperes, volts and coulombs. The constants have the following values:

8.85 x 10^-12 F/m

Permittivity constant

1.26 x 10^-6 H/m

(exactly 4pi x 10^-7)

Permeability constant

The Law of Biot Savart

This handy little law is the foundation upon which most of the air core coil formulas in this site are based:

The current element dl on a current filament contributes a magnetic field, dB, in a direction normal to the plane formed by dl and the vector r.

The good news is that by solving this integral for an arbitrary configuration of current filaments (like a coil, or set of coils) you can compute the magnetic field vector at any point in space.

The bad news is that there is no closed solution to this integral for most interesting configurations of current filaments and vectors r.

Oh well.

These three simple formulas can be derived directly from Maxwell#39;s fourth equation, or Ampere#39;s Law.

Magnetic field due to an infinite, straight current filament

B is the magnetic field, in teslas. The direction of the field is tangent to a circle on a radius r (in meters) from the wire.

is the permeability constant (1.26x10^-6 H/m)

i is the current in the wire, in amperes.

Field inside a straight, infinite, air core solenoid

B is the magnetic field inside the solenoid, in teslas. The direction of the field is parallel to the axis of the solenoid. There is no field outside the solenoid.

is the permeability constant (1.26x10^-6 H/m)

i is the current in the wire, in amperes.

n is the number of turns of wire per unit length of the solenoid, in 1/meters.

Field inside an air core toroid coil

B is the magnetic field, in teslas. The direction of the field is tangent to a circle on a radius r (in meters) from the center of the toroid.

is the permeability constant (1.26x10^-6 H/m)

i is the current in the wire, in amperes.

N is the total number of turns of wire in the toroid.

This simple formula uses the law of Biot Savart, integrated over a circular current loop to obtain the magnetic field at any point along the axis of the loop.

Current loop in cross section view.

B is the magnetic field, in teslas, at any point on the axis of a current loop. The direction of the field is perpendicular to the plane of the loop.

is the permeability constant (1.26x10^-6 H/m)

i is the current in the wire, in amperes.

r is the radius of the current loop, in meters.

x is the distance, on axis, from the center of the current loop, in meters.

Special Case: x = 0

Special Case: x gt;gt; r

Note that this is equivalent to the expression for on axis magnetic field due to a

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MAGNET FORMULAS

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