Relation Between Gauss and Tesla

When a charged particle is moving in a magnetic field, it experiences a force and is defined as magnetic field intensity or magnetic field or magnetic induction. Electromagnetic induction or magnetic field intensity is the production of the emf when an electrical conductor is placed within a varying magnetic field.

Magnetic induction is calculated by using the Lorentz force equation and is given by,

⇒ F = q x v x B x Sinθ ……….(1) 

Where,

F - Lorentz force.

q - Charge on a particle moving in the magnetic field.

B - Magnetic induction or Magnetic field intensity.

On rearranging the equation (1) for B we get,

⇒ B = \[\frac {F} {q}\] x v x Sinθ ………….(2)

Unit of magnetic induction is either Gauss or Tesla depending upon the referred measuring system. Both Gauss and Tesla are interrelated. In order to understand the Gauss and Tesla relation, it is important to understand the definition of individual units.

What Is Gauss?

The unit of magnetic induction in the CGS system is Gauss. Gauss is used for describing the strength of the magnetic field. It is named after German physicist Carl Friedrich Gauss. And is denoted by G.

One Gauss is defined as- Magnetic induction is said to be equal to one gauss if it exerts a force 1dyne on the charge of 1emu moving with velocity 1cm/s perpendicular to the applied magnetic field.

I.e.,

⇒ 1 Gauss = 1G = \[\frac {1dyne} {lemu}\] u x 1cm/s x Sin90

⇒ 1G = \[\frac {1dyne} {lemu}\] x 1cm/s

What is Tesla?

In Physics, Magnetic field strength is measured in several units. Tesla is the unit of magnetic induction as per the international system of units. In other words, Tesla is the SI unit of magnetic induction and it is named after American physicist Nicola Tesla. It is denoted by T.

One Tesla is defined as Magnetic induction is said to be equal to one Tesla if it exerts a force of 1N on a charge of 1C moving with the velocity of 1m/s perpendicular to the applied field.

I.e.,

⇒ 1T = \[\frac {1Ne} {1C}\] x 1m/s x Sin90  

⇒ 1T = \[\frac {1N} {1C}\] x 1m/s

Gauss and Tesla- Relation

Gauss is referred to as the CentimeterGram Second (CGS) unit of the magnetic flux density represented by G which is superseded by Tesla as the International System of Units. The total number of magnetic field lines which are normally passing through a given area is known as the magnetic flux of that area which is represented by H. Now, the amount of magnetic flux, taken perpendicular to the direction of the magnetic flux, through a unit area is known as the magnetic flux density and is represented by B. Unit of magnetic induction is either Gauss or Tesla depending upon the referred measuring system. Both Gauss and Tesla are interrelated. Therefore the magnetic flux density B which is related to a magnetic field H is given by-

B=H

Gauss and Tesla Relationship is Not expressed in Equations

Gauss and Tesla are correspondences which means Tesla supersedes Gauss, therefore their relationship is not expressed in equations is because of the points listed below:

• The CGS system is the family of 3-D unit systems in which the unit of the magnetic flux density is Gauss (G).

• Therefore, gauss can be expressed using the units cm, g, and s.

• The SI unit is the International System of Units in which the unit of the magnetic flux density is Tesla (T).

• It is not possible that tesla is expressed with just m, kg, and s, therefore it includes the unit of electricity which is the 4-D electromagnetic unit.

Gauss and Tesla- Conversion

The magnetic induction units Gauss and Tesla are directly proportional to each other. One can convert Gauss to Tesla and vice versa.  Tesla is a large unit hence it’s preferred to convert into smaller units like Gauss. 

Gauss is the unit of magnetic field strength in Centimeter-Gram-Second (CGS) system which corresponds to three dimensions alone, whereas Tesla is a SI unit covering all seven fundamental units and it corresponds to the fourth dimension thus Tesla can not be described with just Metre-Kilogram-Second system, therefore both units are converted (G to Tesla) into each other. 

To convert Tesla to Gauss begin with the definition of Tesla. We know that one Tesla is given by,

⇒ 1T = \[\frac {1N} {1C}\] х 1m/s ……..(1)

 With the knowledge of unit conversion we write,

⇒ 1N = 10⁵ dyne

⇒ lemu = 10c

⇒ 1C = 10^-1 emu

⇒ 1m/s = 10² cm/s

Substituting the above values in equation (1),

⇒ 1T = 10⁵dyne/10^-1 emu х 10² cm/s

⇒ 1T = 10⁴ dyne/(emu)cm/s = 10⁴Gauss……(2)

Equation (2) gives the relation between Gauss and Tesla.

1 tesla is equal to Gauss multiplied by 10⁴ , thus Tesla is said to be a larger unit in comparison with the other units. Similarly, to convert 1 Gauss to tesla it is to be multiplied by a factor 10^-4.

Therefore, the units Gauss and Tesla are directly proportional to each other and both are used to measure the magnetic field strength.

Solved Examples

1. Convert 20G to Tesla.

Ans: To convert Gauss to Tesla write down the relation between them, given by: ⇒ 1T = 10⁴ Gauss

From the above expression, we can write,

⇒ 1G = 10^-4T

We are asked to convert 15G to Tesla,

⇒ 20G = 20 х 10^-4T

⇒ 20G = 2 х 10^-3T This is the required answer.

2. Convert 3T to Gauss.

Ans: To convert Tesla to Gauss write down the relation between them, given by: ⇒1T = 10⁴Gauss

We are asked to convert 3T to Gauss,

⇒ 3T = 3 х 10⁴ Gauss

This is the required answer.