Sir, in the surface integral you did a mistake by not writing V with E and sir when we come across the topic energy store in an electrostatic field and then in magnetostatic field then we say that volume integral goes up and surface integral goes down. How to understand it with an example.
Would you please mention the location of the video where you think that I have made a mistake. This will help me to respond you accurately. Further, you asked for such an example between the understanding of the surface and volume integral, let's consider an example. Imagine a simple parallel plate capacitor, which consists of two conducting plates separated by a dielectric material. When a voltage is applied across the plates, an electric field is established between them. In this electrostatic field, energy is stored. To calculate the energy stored in the electrostatic field, we can use the volume integral and surface integral. The volume integral refers to integrating the energy density throughout the entire volume between the plates. The surface integral refers to integrating the electric field over the surface area of the plates. When we calculate the volume integral, we integrate the energy density over the entire volume between the plates. This accounts for the energy stored in the electric field throughout the entire space between the plates. On the other hand, when we calculate the surface integral, we integrate the electric field over the surface area of the plates. This accounts for the energy stored at the surface of the plates. The surface integral represents the energy stored in the charges on the conducting plates. In this example, the volume integral represents the bulk energy stored in the electrostatic field, while the surface integral represents the energy stored in the charges on the plates. Similarly, in magnetostatics, when we have a magnetic field and consider energy storage, we can use the same concept. The volume integral accounts for the energy stored in the magnetic field throughout the entire volume, while the surface integral accounts for the energy stored at the surface of the magnetic material. Thanks
at 21:00 Why we take da and not dtau for volume in the spherical shell?
When dealing with the surface of a spherical shell, we use da, if I have understood your question. Thanks
Sir, in the surface integral you did a mistake by not writing V with E and sir when we come across the topic energy store in an electrostatic field and then in magnetostatic field then we say that volume integral goes up and surface integral goes down. How to understand it with an example.
Would you please mention the location of the video where you think that I have made a mistake. This will help me to respond you accurately. Further, you asked for such an example between the understanding of the surface and volume integral, let's consider an example.
Imagine a simple parallel plate capacitor, which consists of two conducting plates separated by a dielectric material. When a voltage is applied across the plates, an electric field is established between them. In this electrostatic field, energy is stored.
To calculate the energy stored in the electrostatic field, we can use the volume integral and surface integral. The volume integral refers to integrating the energy density throughout the entire volume between the plates. The surface integral refers to integrating the electric field over the surface area of the plates.
When we calculate the volume integral, we integrate the energy density over the entire volume between the plates. This accounts for the energy stored in the electric field throughout the entire space between the plates.
On the other hand, when we calculate the surface integral, we integrate the electric field over the surface area of the plates. This accounts for the energy stored at the surface of the plates. The surface integral represents the energy stored in the charges on the conducting plates.
In this example, the volume integral represents the bulk energy stored in the electrostatic field, while the surface integral represents the energy stored in the charges on the plates.
Similarly, in magnetostatics, when we have a magnetic field and consider energy storage, we can use the same concept. The volume integral accounts for the energy stored in the magnetic field throughout the entire volume, while the surface integral accounts for the energy stored at the surface of the magnetic material. Thanks