Gauss Unit Of Magnetic Field Intensity

[Wesley Godinez]

TheInternational System of Units (SI), with the associated International System of Quantities (ISQ), is by far the most common system of units today. In engineering and practical areas, SI is nearly universal and has been for decades.[1] In technical, scientific literature (such as theoretical physics and astronomy), Gaussian units were predominant until recent decades, but are now getting progressively less so.[1][b] The 8th SI Brochure acknowledges that the CGS-Gaussian unit system has advantages in classical and relativistic electrodynamics,[2] but the 9th SI Brochure makes no mention of CGS systems.

A major difference between the Gaussian system and the ISQ is in the respective definitions of the quantity charge. In the ISQ, a separate base dimension, electric current, with the associated SI unit, the ampere, is associated with electromagnetic phenomena, with the consequence that a unit of electrical charge (1 coulomb = 1 ampere 1 second) is a physical quantity that cannot be expressed purely in terms of the mechanical units (kilogram, metre, second). On the other hand, in the Gaussian system, the unit of electric charge (the statcoulomb, statC) can be written entirely as a dimensional combination of the non-electrical base units (gram, centimetre, second), as:

For example, Coulomb's law in Gaussian units has no constant: F = Q 1 G Q 2 G r 2 , \displaystyle F=\frac Q_1^\mathrm G Q_2^\mathrm G r^2, where F is the repulsive force between two electrical charges, QG

1 and QG

2 are the two charges in question, and r is the distance separating them. If QG

1 and QG

2 are expressed in statC and r in centimetres, then the unit of F that is coherent with these units is the dyne.

In the Gaussian system, the speed of light c appears directly in electromagnetic formulas like Maxwell's equations (see below), whereas in the ISQ it appears via the product μ 0 ε 0 = 1 / c 2 \displaystyle \mu _0\varepsilon _0=1/c^2 .

This section has a list of the basic formulae of electromagnetism, given in both the Gaussian system and the International System of Quantities (ISQ). Most symbol names are not given; for complete explanations and definitions, please click to the appropriate dedicated article for each equation. A simple conversion scheme for use when tables are not available may be found inGarg (2012).[5]All formulas except otherwise noted are from Ref.[3]

Below are the expressions for the various fields in a dielectric medium. It is assumed here for simplicity that the medium is homogeneous, linear, isotropic, and nondispersive, so that the permittivity is a simple constant.

Next, here are the expressions for the various fields in a magnetic medium. Again, it is assumed that the medium is homogeneous, linear, isotropic, and nondispersive, so that the permeability is a simple constant.

Therefore, after substituting and simplifying, we get the Gaussian-system formula: E G = q G r 2 r ^ , \displaystyle \mathbf E ^\mathrm G =\frac q^\mathrm G r^2\hat \mathbf r \,, which is the correct Gaussian-system formula, as mentioned in a previous section.

For convenience, the table below has a compilation of the symbolic conversion factors from Table 1. To convert any formula from Gaussian system to the ISQ using this table, replace each symbol in the Gaussian column by the corresponding expression in the SI column (vice versa to convert the other way). This will reproduce any of the specific formulas given in the list above, such as Maxwell's equations, as well as any other formula not listed.[9][10][11][c]

Once all occurrences of the product ε 0 μ 0 \displaystyle \varepsilon _0\mu _0 have been replaced by 1 / c 2 \displaystyle 1/c^2 , there should be no remaining quantities in the equation that have an ISQ electromagnetic dimension (or, equivalently, that have an SI electromagnetic unit).

Imagine encircling an area with a circle of wire. If the magnetic flux in there changes by 1 weber in a second, you'll be able to measure 1 volt induced across the wire. So: 1 weber per second equals 1 volt in the circle of wire. Or: 1 Wb = 1 V s.

Note that nothing is mentioned about the size of the loop of wire. It doesn't matter if the loop of wire is one inch or one meter across. If you're measuring 1 volt across the wire, the magnetic flux is changing by 1 weber per second in there.

Unlike Magnetic Flux above, the Flux Density defines some size for the loop of wire in that example. Flux Density is a measure how many webers are squeezed into some area. In fact, webers per square meter is the unit for flux density. By definition, 1 weber per square meter (Wb/m2) = 1 tesla (T).

Here's a confusing part: Many people call this, "field strength." We often refer to field strength in gauss. Technically, we should probably use the term, "magnetic flux density," though it's much more commonly called, "field strength."

There's another, somehow different unit for field strength. It is commonly expressed in amperes/meter (A/m) or oersted (Oe). How is this different than the flux density expressed in gauss or tesla? Why are there 2 different units? Are they the same thing?When we think about the "field strength" at the surface of a magnet (the Surface Field), we're looking for something expressed in gauss. For example, a D82 disc magnet has a surface field of about 2,952 gauss. Stick a magnetometer on the surface of this magnet and we'll measure magnetic flux (often called field strength). So what's this oersted thing all about?

When manufacturing permanent magnets, magnet material is magnetized by exposing it to an external magnetic field. In practice, this means the magnet material is placed in a fixture, sitting inside a big coil of wire. For a brief instant, a strong magnetic field is created by running a lot of electric current through the coil of wire. The magnet is exposed to a magnetic field strong enough to magnetize the magnet. Historically and commonly, this field strength is expressed in A/m or Oe.

The demagnetization curve of a magnet material describes it magnetic properties. It describes how much field strength is required to magnetize a magnet, and more importantly for magnet users, how the magnet will perform. One axis of this curve is B (flux density expressed in gauss, comes from the magnet itself) and the other axis is H (the applied or external magnetic field in the magnetizing fixture, expressed in Oe). You can find BH curves for various magnet grades on our BH curves page. The second half of our Magnet Grades article has a great step-by-step description about how these curves are measured.

In some ways, you might argue that these things are really the same. They are in many cases, but not always. There are times when saying that 1 oersted is like 1 gauss works out well. Since B = H, it's a fair assumption if the material is air. If you dive into the physics and math of these properties, you'll find a lot more interesting, complex stuff going on. There's a lot more to learn than we'll go into here in a simple unit converter!

BHmax is a single number that describes the strength of a magnet. It is expressed in mega gauss oersteds (MGOe). It is the product of B x H on the demagnetization curve, at the location where this number works out to be the highest. In other words, it's the area shown in the box under the BH curve.

When comparing neodymium magnets, we find that the pull force relates directly to this number. If everything else is equal, a magnet with a BHmax that's 10% higher will have about a 10% higher pull force.

This number is great for comparing various neodymium magnet grades, or even between neodymium and samarium cobalt magnets. It is less useful when comparing very different magnet types, such as neodymium magnets vs. Alnico, since the Alnico demagnetization curve is so different.

Moment is an engineering term used to describe a torque value. For example, if you turn a bolt with 2 ft long wrench, applying 10 lb of force on the end of the wrench, you would be turning the bolt with 10 x 2 = 20 ft lb of torque[1]If you're metrically inclined, you might describe a 44.5 Newton force on a 0.61 meter wrench, yielding a 27.1 N m torque..

By definition, the magnetic dipole moment is the turning moment (the torque that's trying to rotate the magnet) that a magnet "feels" in a given magnetic field. Imagine placing a magnet inside a space that has a strong magnetic field, like the inside of an MRI machine. The magnetic dipole moment is how much torque will try rotating the magnet to align with the MRI's field.

What's a more practical, real world example? Consider a compass needle. The needle itself is a magnet. If it's not pointing north (aligning itself with the earth's magnetic field), the needle will feel a torque trying to rotate it towards north. It's a fairly weak torque, because the earth's magnetic field is so weak (about 0.5 gauss).

Units for dipole moment make sense with this mechanical description: newton meters per Tesla (N m / T). That's newton meters (the torque, force times distance) per Tesla (the field). If you're not used to metric units, you might say the same thing as pound-feet of torque per gauss (lb ft / G). Though technically correct, we've never seen anyone use this unit.

Much more commonly, this unit is expressed in Ampere square meters, A m2. Electrical engineers and physicists find this useful. It's an easy conversion: 1 A m2 = 1 N m / T. You can calculate the dipole moments value yourself using this formula dipole moment formula. Or use our online Pull Force Calculator, which calculates the dipole moment.

Magnetic field strength is a measure of the intensity of a magnetic field in a given area of that field. Represented as H, magnetic field strength is typically measured in amperes per meter (A/m), as defined by the International System of Units (SI). Ampere and meter (or metre) are SI base units constructed from the SI's defining constants. Ampere is the measure of electric current, and meter is the measure of length.

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