MAGNETO STATIC BOUNDARY CONDITIONS

[Audio] Hello everyone . Today I am here to explain about magnetostatic boundary conditions..

[Audio] As we can see in the video there is a magnetic wave passing through two media. Boundary conditions can be useful in evaluating magnetic line passing through different mediums..

[Audio] As we know there are boundary conditions for electric field. There are some boundary conditions for magnetic field also . It defines as when magnetic field passing across two media ,this concept explains about the discontinuity of magnetic flux among them..

[Audio] While proving these conditions we consider a sheet of area that separates two different media with different magnetic fields..

[Audio] We can calculate these boundary conditions at any angle of the mediums that separate mediums. To make the concept more understandable we will deal mainly with two cases which are tangential and normal directions..

[Audio] First let us see normal conditions. Consider two mediums having separate magnetic fields. Let us consider a sheet between two mediums . it is having magnetic fields perpendicular to sheet. Let magnetic field in medium 1 be BN1 and that of medium2 is BN2 respectively. Now let us take a small cuboid shape element of the sheet which will have six faces. Consider Gauss law for verification..

[Audio] As we know gauss law for magnetic field that states magnetic flux through any closed surface is zero..

[Audio] We can apply it for each face of cuboid to evaluate Gauss law to find relationship between two fields..

[Audio] On applying gauss law for each and every face , we can see in the presentation that left , right, front, back, their's integral over b dot d s that is Gauss law becomes zero. This is because as we considered sheet it is only two dimensional and it's z component is negligible . So the are ds will be approximately zero. Now we have only two faces namely top and bottom which are parallel to each other .So, their area will be equal. On cancelling out them we have bn1 equals to bn2..

[Audio] The above representation proves that in normal direction there will be no discontinuity of magnetic field. That means magnetic field on sheet in both directions will be same..

[Audio] Now let us see tangential conditions. Consider tangential direction among the 2 mediums depicted above..

[Audio] As the sheet is tangential to each other, now the sheet is in the direction of magnetic field. Consider ampere's law..

[Audio] As we know , that Ampere's gives relationship between current and the magnetic field it generates which mathematically represented as integral over h dot length that equals current enclosed..

[Audio] Applying ampere's law on every side which equals to current enclosed and to magnetic constant k multiplies delta x . As sides b to c and d to a becomes zero. This is because as they are perpendicular to magnetic field their dot product becomes zero . Remaining components equals k delta x , on further calculation the difference in magnetic field strength h1 minus h2 gives magnetic constant k..

[Audio] Therefore , we conclude that in tangential condition there will be discontinuity in magnetic field that equals k..

[Audio] Thank you for giving this opportunity .. Thank you text on white background. Calligraphy lettering Vector ....