why the flux of magnetic field over a closed surface always zero?

Asked by yashrajgharte24.12dgatl | 24th Aug, 2021, 07:23: AM

Expert Answer:

We get magnetic field induction due to parallel alignment of magnetic dipoles . Magnetic monopole does not exist.
 
Magnetic field lines from magnetic dipole are closed , i.e, field lines starting from dipole will end at same dipole. 
 
Hence if we consider a closed surface that encloses magnetic dipoles, then  flux is coming out at some region of surface
 
and flux enters towards surface in other region  so that net flux through the closed surface is zero.
 
The concept of net flux over a closed surface is zero is expressed mathematically as follows.
 
begin mathsize 14px style surface integral B with rightwards arrow on top times stack d a with rightwards arrow on top space equals space triple integral space open parentheses nabla times B with rightwards arrow on top close parentheses space d v space equals space 0

end style
( In vector analysis, integration of vector function over closed surface equals integration of divergence of vector function
over enclosed volume of the closed surface )

Hence we get the Maxwells equation begin mathsize 14px style nabla times B with rightwards arrow on top space equals space 0 end style

Answered by Thiyagarajan K | 24th Aug, 2021, 08:19: AM