Ampere's Circuit Law

[Audio] Hello everyone, today we are going to discuss about ampere circuit law..

[Audio] So the given question is about the magnetic flux density due to infinite line current from amperes circuit law, as you can see in the given animation there is a infinite long current carrying conductor and it generates the magnetic field around it..

[Audio] Now let us know about what is ampere circuit law ,this law states that the line integral of tangential component of magnetic field intensity around a closed path is same as the net current enclosed by the path. and you can also see the mathematical representation in the given picture. The closed integration of H dot DL is equals to, the total current enclosed..

[Audio] Let us know understand the relationship between magnetic field intensity and the magnetic flux density. In free space the relationship between b and H is given as b equals to mu times of h. Where mu represents the permeability of free space and the value is 1.25663706 × 10-6 m kg s-2 A-2.

[Audio] Right hand thumb rule. It states that if you imagine holding a current carrying wire in your hand, the direction of your thumb shows the direction of the current and the direction of the fingers curl shows the direction of the magnetic field. As you can observe in the animation..

[Audio] in this animation you assume that the direction of the current is towards you. so when you placed a compass around this current carrying wire, the needle of the compass deflect towards the direction of the magnetic field, by the deflection of these needle we can conclude that it is a circular path. Now let us derive the formula for magnetic field due to infinite line current..

[Audio] Here the first picture represents front view of the current carrying conductor and second picture represents the top view, now consider a small part of DL and the direction of B. As we know from the ampere circuit law closed integration of h dot dl equals to I. By substituting b equals to mu not times h in the above equation we get closed integration of b dot dl equals to mu not Times of I. As the angle between b and DL is zero. we get b times closed integration of DL. Now the closed integration of dl gives the circumference of the circle, which is 2 pi R..

[Audio] By simplifying we get the equation as b equals to mu not Times I divided by 2 pi r. Therefore the magnetic flux density due to infinite line current from ampere circuit law is given as b equals to mu not times I divided by 2 pi r. Where, b is the magnetic field, mu not is the permeability of free space, I is the current in the wire, R is the distance from the wire..

[Audio] That's the end of this video, I hope you understand the topic, Thankyou..