 instead of technology, Sholaboon in electronics department. In this video lecture, I am going to discuss about the Maxwell's equation in part 1, learning outcomes. At the end of this lecture, students are able to derive the Maxwell's equation in integral form and in a point form using Faraday's law and Ampere's law. Now, what are Maxwell's equations? Maxwell's equations describes the relationship between the changing electric field and magnetic field. Maxwell's equations are the extension of the known work of Gauss, Faraday's and Ampere. Now, let us see how electric field and magnetic fields are related. Let us consider a current carrying filament placed across the magnetic field. Will there be a magnetic field around this capacitor? Yes, it is observed by the Maxwell's that the changing magnetic field flux produces the electric field and changing electric flux produces the magnetic field, which are nothing but a Faraday's law and Ampere's law. The Faraday's law which is stated as the electromotive force around the closed path is equal to the negative rate of change of magnetic flux enclosed by that path, which is mathematically given by emf is equal to minus d phi by dT, now. But what is emf? Emf is nothing but a electric field across the length. Magnetic flux is the magnetic flux density across the surface. When we substitute these two terms in equation 1, we will get this equation 2, which is nothing but a Maxwell's equation in integral form derived from the Faraday's. Now, when we apply the stroke theorem to the right hand side of equation 2, then the integral E dL will be replaced by del cross E bar over the surface. And when we equate that, then both sides are with respect to the surface. Then we reduce that equation to del cross E bar is equal to minus dou B by dou T, which is nothing but a Maxwell's equation derived from Stroke's law in point form. Ampere's law. What the Ampere's law says? The Ampere's law states that line integral of magnetic field intensity along the single closed path is always equal to the current enclosed by that path. Let us see in the mathematical how the statement is given. Close integral of H dL, E L is equal to I, which is, but what is I? I is nothing but a current density over the surface, that is integral of J dS. Now, the J is nothing but a current density, which is due to the current due to the resistance and current due to the capacitance. The current due to the resistance is given by sigma E bar and current in a capacitor is given by dou D by dou T. When we substitute the value of J of C and J of D, the equation will be getting the equation 4. In this equation, when we equate them, we are getting the Maxwell's equation in integral form derived from the Ampere's law. When we similarly, when we apply the Stroke's theorem to the equation on the right hand side in equation 4, then integral H dL will be replaced to a integral over the surface del cross H bar, then we equate that equation. These are the equations, which are relating over the surface. Then it is reduced to del cross H bar is equal to sigma E bar plus dou D by dou T. This is nothing but a Maxwell's equation derived from the Stroke's law in point form. Now, let us see, observe. If you observe here, there are two vectors, which are representing with the red line and blue line. The blue line are indicating the vector field of electric and red lines are indicating the vector field in a magnetic field. Now, let us consider a loop, current canning a loop placed, which is shown by green solid line. This green solid line, which is nothing but a special position where we are representing. If you observe that, this is nothing but a rate of change of the magnitude of the magnetic field with respect to time and it is associated with the electric field. It is parallel to the electric field. Then this is nothing but a Maxwell's Faraday's law. If you observe the LO path, which is a special position associated with the electric field, if you see that it is parallel with the magnetic field that this is nothing but a rate of change of the electric field, which is nothing but a Maxwell's Ampere's law. In this equation, it is associated with following the Faraday's law as well as the Ampere's law. Let us assume, imagine a wave of electric field in z direction. Then the moving electric field leads to the change in x direction in which the wave is propagating to the rate of change of the magnetic field. And the changing magnetic field leads to the change in the rate of change of the magnitude of the electric field in a x direction, which are nothing but wave equations for the Maxwell's. That is why, thus we conclude that the Maxwell's equations provide the mathematical background for the studying of the electromagnetic waves. The remaining part of this Maxwell's equations, we will be studying in a part 2 lectures of the Maxwell's equation. The references which I had referred for this are listed over here. Thank you.