kolahalb
Junior Member level 1
What is the wrong in the proof that there is no magnetic field?
We know:
div B=0 and B=curl A where B is the magnetic field and A is its vector potential
Then,∫div B dV=0=∫B.n dA(divergence theorem)
Thus, 0=∫(curl A).n dA
=∫A.dr(Stokes' theorem)
The last will be a cyclic integral.
Since the cyclic line integral is zero,A is conservative;
or,A=grad f
Then,B=curl A=curl grad f=0
or,B=0
I think the problem lies between the equality in Stokes' theorem.In original Stokes' theorem LHS is a non-cyclic integral whereas here it comes directly from divergence theorem and is a cyclic integral...
Please let me know if i am correct;if not,then where did I go wrong.
Thank you in advance
We know:
div B=0 and B=curl A where B is the magnetic field and A is its vector potential
Then,∫div B dV=0=∫B.n dA(divergence theorem)
Thus, 0=∫(curl A).n dA
=∫A.dr(Stokes' theorem)
The last will be a cyclic integral.
Since the cyclic line integral is zero,A is conservative;
or,A=grad f
Then,B=curl A=curl grad f=0
or,B=0
I think the problem lies between the equality in Stokes' theorem.In original Stokes' theorem LHS is a non-cyclic integral whereas here it comes directly from divergence theorem and is a cyclic integral...
Please let me know if i am correct;if not,then where did I go wrong.
Thank you in advance