 instead of technology working in the electronics department as a associate professor. In this video lecture, we are going to discuss on Maxwell's equation in a part 2. Learning outcomes at the end of this session students are able to derive the Maxwell's equation in integral form and in a point form using the Gauss law and represent the Maxwell's equation in different field also able to solve a related problems. Let us recall what we have discussed in a part 1. Maxwell's equations are nothing but describing the relationship between the changing electric field and magnetic field. Maxwell's equations are extensions of the work of Gauss law, Faraday's law and Ampere's law. What the Gauss law states in an electric field that is a max electric flux passing through any closed surface is equal to the total charge enclosed by that surface that is psi is equal to q where psi is nothing but an electric flux and q is a charge enclosed by that surface. But what is psi? Psi is nothing but a change in the electric flux density over the surface and q is nothing but a charge distribution over the volume. When we substitute this psi and q in equation 5, the equation will reduce to this part and this equation number 6 is nothing but a Maxwell's equation in integral form derived from the Gauss law. Now let us see the Gauss apply the divergence theorem to the RHS sorry LHS in the equation 6. When we apply the divergence theorem to the right hand side then DDS will be replaced by dow del dot d bar over the volume and when we substitute that it will be equating the both the sides are equating over the volume and that equating that will be reduced to the del dot d bar is equal to rho V which is nothing but a Maxwell's equation derived from the divergence theorem in a point form. Now Maxwell's equations in a deriving from the Gauss law which is stated in the magnetic field this with the statement of the Gauss law in magnetic field is the magnetic flux passing through any closed surface is always equal to 0 which is mathematically given by psi over the magnetic field is always equal to 0. But what is psi? Psi is nothing but a magnetic flux over the surface which is given by integration over the surface B DOS magnetic flux density. The magnetic flux density is equated to 0 over the surface this will give you the Maxwell's equation in integral form derived from the Gauss law. When we apply the divergence theorem to the LHS integral over the surface B DOS will be nothing but integral over the volume B del dot B bar dV and when we equate them to the 0 then del dot B bar will be equal to 0. This is a Maxwell's equation derived from the divergence theorem in a point form. Now we are observed the Maxwell's equation in integral form as well as in a point form. The Maxwell's equations in the integral form governs the independence of certain field and source quantities associated with the region in the space, surface and volume. And Maxwell's equation in a point form relates the characteristics of the vector field at any given point to the another and the source density at that point which is represented by equations in Faraday's law and Gauss law and M.P.S. law. If we summarize all the equations which we have studied in the Maxwell's equation part 1 and part 2 are summarized over here. These are the column 2 represent the Maxwell's equations which are in the integral form and Maxwell's equations in a point form. When we this we are setting as a Maxwell's equation in general form which are derived from Faraday's law, M.P.S. law, Gauss law in electric field, Gauss law in magnetic field. When the Maxwell's equations how this Maxwell's equations are represented in a free space. In a free space sigma and rho v is equal to 0. Now when we replace the sigma and rho v in the previous general equation then these 4 equations will be replaced. This is a representation of the Maxwell's equation in free space by considering sigma and rho v is equal to 0. Another table the Maxwell's equations which are in a static field for this in the general equation we are replacing the dow by dow t is equal to 0. As we are saying it is a static field that is why dow by dow t will be equal to 0. When we replace the dow by dow t which is there in the general equation then these 4 terms will be replaced. This table represents the Maxwell's equation in static field. Now Maxwell's equations in harmonically time varying field that is dow by dow t is equal to j omega. Wherever there is a dow by dow t we will replace it with the j omega where omega is nothing but a 2 pi f. Now the Maxwell's equations after substitution dow by dow t is equal to j omega these 4 equations are been replaced. This table shows the Maxwell's equation in harmonically time varying field. Now pause the video let us solve this problem consider sigma is equal to 0 epsilon is equal to 2.5 epsilon 0 mu is equal to 10 mu 0 where epsilon 0 is 8.85 into 10 raised to minus 12 and the value of mu 0 is 4 pi into 10 raised to minus 7. Now determine whether the following pairs of the field satisfies the Maxwell's equation. Substitute the value of e bar and substitute the value of h bar which are the equations we are seeing in the general form. Yes this pairs of the this pair satisfies the Maxwell's equations. When we substitute these two equations in the then first part will also be satisfied second part will be that is why these equations will satisfy the Maxwell's equation. These are the references which are referred for this chapter. Thank you.