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Ampere’s circuital law and its derivation

What is ampere’s law?

According to this law “The line integral of magnetic field B along a closed path due to current is equal to the product of the permeability of free space and the current enclosed by the closed path”.

Mathematically it is expressed as:

amp

Where

μ0=permeability of free space

i=current flowing through the conductor.

Proof:ampere's law

Consider a straight conductor in which current i is flowing.The current produces the magnetic field B around the conductor.The magnetic field lines are in the form of concentric circles.

Ampere showed that the flux density B at any point near the conductor is directly proportional to the current i and inversely proportional to the distance ‘r’ from the conductor ,so:der of amp lawamp

Where  is the length of the path called circumference of the circle.

Divide the circle representing the magnetic field line into large number of small elements each of length dl.The quantity B.dl is calculated for each element as:

B.dl=Bdlcos= Bdlcos0=Bdl

For complete circle:

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Integral form of ampere law:

integral form of ampere law

Differential form of ampere law:

Since the integral form of ampere’s law is:

diff form of ampere law

The above relation is known as differential form of ampere’s circuital law.

What is ampere's law? According to this law “The line integral of magnetic field B along a closed path due to current is equal to the product of the permeability of free space and the current enclosed by the closed path”. Mathematically it is expressed as: Where μ0=permeability of free space i=current flowing through the conductor. Proof: Consider a straight conductor in which current i is flowing.The current produces the magnetic field B around the conductor.The magnetic field lines are in the form of concentric circles. Ampere showed that the flux density B at any point near the conductor is…

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One comment

  1. muy interesante y fascinante publicación de ciencia física.

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