Relation Between Gauss and Tesla - A Complete Guide

Gauss and Tesla are units widely used for measuring the magnetic flux density essential in the study of electromagnetism. Tesla, the SI unit, represents larger magnetic fields; in contrast, Gauss is a CGS unit for smaller fields. The relation between them, that is, 1 Tesla = 10,000 Gauss, establishes a connection between the two systems of measurement. It becomes more important when one has to analyze a magnetic field for various applications in physics.

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What is Gauss?

Gauss is the unit of magnetic induction in the CGS system. It is named after Carl Friedrich Gauss, a famous German physicist.

The base unit of Gauss is, $1 \mathrm{~cm}^{-1 / 2} \mathrm{~g}^{1 / 2} \mathrm{~s}^{-1}$

1 gauss is defined as 1dyne of force which exerts on a charge of 1emu which moves in velocity of 1cm/s in the magnetic field perpendicularly.

What is Tesla?

Tesla is a unit of magnetic field intensity or magnetic induction. In other words, the SI unit of magnetic induction is Tesla or it. It is usually denoted by T. This unit is named after Nikola Tesla, the famous American physicist.

Tesla $=K g s^{-2} A^{-1}$

1 Tesla is defined as the intensity of a magnetic field which generates a force of 1Newton per current of 1Ampere and a conductor of one meter.

So 1 Tesla is equal to 1N of force which exerts on coulomb of charge of 1C which moves in velocity of 1m/s in the magnetic field perpendicularly.

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Relation Between Gauss and Tesla

We are all aware of the attraction and repulsion forces upon a charge entering an electric or magnetic field. Now suppose some moving charge particle enters into the magnetic field then the size of the force experienced or acting on that charged particle is called the intensity of magnetic field or sometimes we will call it Magnetic Induction, which can be calculated using Lorentz as:

$$
F=q(V \times B)
$$

or, $F=q V B \operatorname{Sin} \theta$ $\qquad$ (1)

Here, F = Lorentz force(F)
$q=$ magnitude of the charge on moving particle (C)
$\mathrm{V}=$ velocity of moving particle
$B=$ magnitude of magnetic field intensity
$\& \theta=$ angle between the velocity vector and magnetic field vector.
From equation (1), we can derive, the magnitude of magnetic field intensity as,

$$
B=F / q V
$$
And, the units of this magnetic field intensity are Gauss or Tesla, depending upon the units system considered for the calculation and both the units are also interrelated to each other.

This relation between Gauss and Tesla helps us convert from one unit to another and vice versa and will be proved to be convenient while doing calculations.

The formula of Gauss Law and Tesla

Tesla is a bigger unit than Gauss. The interrelations between Gauss and Tesla can be expressed mathematically as,

From Tesla to Gauss

• 1 Tesla $=10^4$ Gauss

From Gauss to Tesla

• 1 Gauss $=10^{-4}$ Tesla

Here are some of the most commonly used units for the measurements of magnetic flux density.
1 Tesla $=10,000$ Gauss
100 Gauss $=0.01$ Tesla

Conversion of Gauss to Tesla or Tesla to Gauss

The Conversion of Gauss to Tesla or Tesla to Gauss is quite simple as both are directly proportional. Tesla is a big unit that can be converted into small units.

1 tesla is equal to how many gauss?

1Tesla is 1N of force which exerts on coulomb of charge of 1C which moves in velocity of 1m/s in the magnetic field perpendicularly.

1Tesla = 1N /(1C * 1m/s)

We know that

1N = 10⁵ dyne

1C = 10^-1 emu

1m/s = 10² cm/s

1Tesla = 10⁵ dyne/(10^-1 emu*10² cm/s)

1Tesla = 10⁴ dyne/(emu*cms)

1Tesla = 10⁴ gauss

Therefore, one tesla is equal to 10⁴gauss.

Conversion of 1 gauss to tesla:

1 gauss is equal to 10^-4 Tesla.