The discussion revolves around the conditions under which terms of a surface integral can be neglected, particularly in the context of large surfaces and the behavior of a vector field at infinity. Participants explore the implications of the vector field's decay rate relative to the growth rate of the surface area.
Participants express differing views on the implications of the decay rate of the vector field relative to the surface growth, indicating that the discussion remains unresolved regarding the conditions under which terms can be neglected.
The discussion highlights the dependence on specific assumptions about the decay rates of the vector field and the growth of the surface, which are not fully resolved.
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##