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Relation Between Gauss and Tesla

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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Gauss is referred to as the CentimeterGram Second (CGS) unit of the magnetic flux density represented by G which is superseded by Tesla as the International System of Units.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.

Some of the Commonly used Values of the Magnetic Flux Density

1 Tesla=10,000 Gauss


100 Guass=0.01 Tesla


Gauss and Tesla- Formula      

The mathematical representation of Gauss and Tesla can be done by-

1 Tesla=104Gauss


1 Gauss=10-4Tesla


Gauss (G) can be defined as one maxwell per square centimeter which is-


1 G=cm-1/2.g1/2.s-1


Tesla (T) can be defined as one weber per meter square which is-


1T=m-1/2.kg1/2.s-1

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.

FAQs on Relation Between Gauss and Tesla

1. How Many Tesla is Equal to 1 Gauss or How Many Gauss is Equal to 1 Tesla?

Both questions can be answered by writing the relation between them given by,

⇒ Tesla = 104 Gauss

⇒ 1Gauss = 10-4 Tesla

2. Why do We Need the Conversion of Units?

Gauss is the unit of magnetic induction in the CGS system whereas Tesla is the SI unit of magnetic induction. Since Gauss is a measurement done in three dimensions, it is easy to do the mathematical calculation as compared with the Tesla as it corresponds to seven fundamental units and its measurement leads to the 4th dimension. Thus it is always preferred to convert g to tesla.

3. Is 1 Gauss is Equal to 1 Tesla?

No. 1 gauss =0.0001 Tesla.

4. What are Some of the Properties of Magnetic Flux?

Properties of the magnetic flux are listed below-

  • Through a closed surface, the magnetic flux is zero always while in the case of open surfaces, it is not zero.

  • A closed is always formed by them.

  • Starting from the north pole, the magnetic flux ends in the south pole always.

  • The magnetic lines of force can never intersect.

  • These are parallel to each other always

  • These are always in the same direction and have the tendency to repel each other.

5. What is the Mathematical Representation of Magnetic Flux?

Magnetic flux can be given by- фB=B.A. Now suppose, the magnetic field is constant then the magnetic flux which is passing through a plane having an area A will be- фB=BA cos; where B is the magnetic field and is representing the angle through which the magnetic field lines are passing in a plane. The SI unit for Magnetic Flux is known to be as Weber represented as Wb and which equals to 1 Tesla x 1 m2. The fundamental and the CGS units of Magnetic flux are V/s and Maxwell (Mx) respectively where the relation between the SI and CGS unit is 1 Wb= 108 Mx.

6. What are Some of the Differences between the Magnetic Field and Magnetic Flux?

The area which is around the magnet is referred to as the magnetic field of the magnet wherein the charged particles which are moving experience the force of magnetism while the number of magnetic field lines which are passing through a surface is referred to as the magnetic flux. The strength of the magnetic field is shown by the magnetic flux within a specific area. The mathematical representation of magnetic field and magnetic fluxes are F=qvB and фB=B.A respectively and their units are Tesla and Weber respectively.

7. What are Some of the Conditions in Order to Obtain Maximum and Minimum Magnetic Flux?

The angle through which the magnetic field lines are passing the surface plays an important role in obtaining the maximum and the minimum flux. If 90° is the angle between magnetic field lines and the surface, a very low or maybe zero magnetic flux is produced, it is because- =90°. According to the formula of magnetic flux- фB=B.A cos90°=0. Now if the angle is 0° between the magnetic field lines and surface, maximum magnetic flux is produced. =0°According to the formula of magnetic flux- фB=B.A cos0°=BA.

8. What are Some of the Differences between Magnetic Flux Density and Magnetic Field Intensity?

The magnetic field intensity and the magnetic flux density are both representatives of the strength of the magnetic field but the difference is that the magnetic field intensity is considered are the external source and a representative of the magnetizing force which is pumped by it into the surrounding medium while the magnetic flux density is considered as the representative of the effectiveness of the medium utilizing the magnetic force or the amount of the magnetic field which is induced into the medium.