ELECTRIC FIELD , BIOT SAVART'S AND AMPERE'S CIRCUITAL LAW

The topic we will discuss today that is actually based on current and magnetism. We all know about electric current which is familiar to us and we know about it so much and we also know about magnets and its behavior but in this topic we will see some phenomenon happened due to electromagnetism means magnetism due to current.

Electromagnetism-The magnetism due to flow of electric current in the conductor is known as Electromagnetism.

We had studied a chapter “current” in class 10(NCERT). There we had read many examples of electromagnetism like working of motor and generator etc. and we had also practicalled an experiment that was – when a current carrying wire has passed through a cardboard and iron dust spread on it, then iron dust gets arranged in concentric circle around the wire.

                       

Here , we can see iron dust gets arranged due to magnetic behaviour of electric current . And the direction of current is find by

Right hand thumb rule:-

According to Right thumb rule ,when we curl our fingers of right hand and raise our thumb then thumb points the direction of current and the curled fingers shows the direction of magnetic field.

What is Magnetic field ?

– The region or space  in which magnetic force can be experiencd is known as magnetic field.

• ·         It is denoted by B which is vector quantity.
• ·         Its si unit is T(Tesla).

   To know more about dimensions of various physical quantity  Click here>>

     Till now we are studying only basic , Now we will know about Boit savart’s law and  Ampere circuital law.

What is Biot savart’s law ? Why we use it? So, lets find out..

 Biot savart’s law

It is used to find strength of magnetic field at any point due to current carrying wire at some distance.

Consider a wire of length l , Current in the wire is I . Let a point p where we have to find magnetic field which is r distance apart from the wire at θ angle.

We are considering very small magnetic field dB due to current I flowing in the wire of very small length of dl.

We know that Magnetic field is directly proportional to

• ·       dB ∞  I (current)
• ·      dB ∞  dl (length of wire)
• ·      dB ∞  1/r² (distance from wire)
• ·      dB ∞  sin θ (angle)

Then  dB ∞  (I dl sin θ)/ r²

            dB=(K I dl sin θ)/ r²

Where K is proportionality constant.

And , value of K = μ₀/4 π =10^-7  Tm/A.

And, μ₀  is absolute permeability of free space and its value is 4 π x 10^-7  Tm/A. It is the degree of magnetization of a material in response to a magnetic field.

·         Formula:-

1.       Magnetic field due to infinitely long straight wire carrying current using biot savart law= K 2 I / r

2.       Magnetic field on the axis of a circular loop carrying current = μ₀I/2r

The direction of magnetic field is same as that of the cross product  of dl and r should be. And it is perpendicular to the inside the plain and represented by CROSS sign.

Ampere circuital law-

It states that line integral of magnetic field around any closed path in free space is equal to absolute permeability (μ₀) times the net current is passing through any surface inclosed by closed path.

Let a infinitely long straight conductor carrying current I in the wire. The magnetic field lines are produced around the conductor as concentric circle.

Then acoording to biot savarts law ,

Magnetic field at point p

= K 2 I / R

=(μ₀ 2I )/4πR

Now, Draw a circle of radius R around the wire which is also known as amperen loop . let a small element of length dl on the circle.

Since dl and B are in same direction . then angle θ between them will be 0.

Hence, B.dl cos 0 = B.dl

We can find the line integral by integrating B.dl  in the closed loop

=∮ B.dl

=∮ (μ₀ 2I )/4πR dl

= (μ₀ 2I )/4π R  ∮ dl       (we are only intergrating dl length elemet to form circle)

= (μ₀ 2I )/4π R  x 2πR    (total length of dl length element = perimeter of the circle)

= μ₀ I 

  

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