Okk got it ...thanks @OrodruinOrodruin said:The field ##\vec A## is assumed to go to zero at infinity at a rate faster than the rate at which the surface grows.
But if the rate at which the vector field ##A## goes to zero at infinity is slower than the rate at which the surface grows ,then also it would be zero ,isn't it??Orodruin said:The field ##\vec A## is assumed to go to zero at infinity at a rate faster than the rate at which the surface grows.
Ok the field decreses as ##\frac{1}{r^2}## and the spherical surface element centered at the point charge grows as ##r^2sin\theta d\theta d\phi##Orodruin said:No. You need the assumption of the field going to zero fast enough. Take the example of the field of a single point charge.
And so the integral is not zero.Apashanka said:Ok the field decreses as ##\frac{1}{r^2}## and the spherical surface element centered at the point charge grows as ##r^2sin\theta d\theta d\phi##
An integral equation for large surfaces is a mathematical equation that relates the values of a function on a large surface to the values of the function on a smaller surface. It is commonly used in the field of mathematics and physics to solve problems involving large surfaces, such as finding the electric potential on a conducting surface.
An integral equation for large surfaces is different from other types of equations because it involves integrating a function over a large surface instead of solving for a specific value. This allows for a more general solution that can be applied to a variety of surface shapes and sizes.
Some common applications of integral equations for large surfaces include solving problems in electrostatics, heat transfer, and fluid dynamics. They are also used in image processing and computer graphics to model and analyze large surfaces.
Integral equations for large surfaces are typically solved using numerical methods, such as the boundary element method or the method of moments. These methods involve discretizing the surface into smaller elements and then solving the resulting system of equations.
One limitation of using integral equations for large surfaces is that they can be computationally intensive, especially for complex surfaces. Additionally, they may not provide an exact solution and may require simplifying assumptions to be made. As such, they should be used in conjunction with other methods for more accurate results.