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  GR8677 #79
Problem
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Verbatim question for GR8677 #79
Electromagnetism}Field Lines

The Maxwell Equation that states ``No monopoles" requires that the divergence of the magnetic field be 0, or more elegantly, \nabla \cdot \vec{B} = 0. The problem asks for fields that violate this condition, so the condition to look for now is \nabla \cdot \vec{B} \neq 0.

(A) \vec{B}=\pm Const ... divergence is 0

(B) \vec{B}=\pm Const ... divergence is 0

(C) this does not explicitly require the divergence to be 0.

(D) this is a non-zero divergence, as the field lines diverge outwards from a source.

(E) this is \nabla \times \vec{B}\neq 0... doesn't necessarily state anything about \nabla \cdot \vec{B}


See below for user comments and alternate solutions! See below for user comments and alternate solutions!
Alternate Solutions
ramparts
2009-11-06 10:39:09
Another way to think of this problem: grad B = 0 is the Maxwell's equations way of saying "no magnetic monopoles". D is the one that clearly shows a monopole being there :)Alternate Solution - Unverified
Comments
livieratos
2011-11-08 06:10:01
i wonder how things would be affected if ever a magnetic monopole was discovered... would there just be a q_m (magnetic charge in a sense) on the right side of the equation or would things be much more complicated than that...NEC
ramparts
2009-11-06 10:39:09
Another way to think of this problem: grad B = 0 is the Maxwell's equations way of saying "no magnetic monopoles". D is the one that clearly shows a monopole being there :)
IRFAN
2011-08-18 03:10:32
plz use div.B instead of grad b

pam d
2011-09-26 21:36:28
smh
Alternate Solution - Unverified
anmuhich
2009-03-21 13:58:00
Have a visual understanding of what the "divergence" of a field is. D is the only answer which clearly has field lines which are diverging, wherease the other ones could curl back around on themselves eventually (or do).NEC
ArtifexR
2009-02-23 19:53:06
Another way to consider the problem is to remember that the equation is the equivalent of Gauss' Law for Magnetism. Hence, the total magnetic flux through any Gaussian surface must be 0. The only diagram which definitely has a flux through the walls of the box is diagram D.
insertphyspun
2011-02-21 19:52:31
Absolutely. The integral form of \bigtriangledown\cdot B=0 is derived using the divergence theorem.

\int\bigtriangledown\cdot BdV=\int\int_{S}B\cdot dS=0

Thus, all lines within the boxes that are drawn must enter and leave. This is not true for D.
NEC
ArtifexR
2009-02-23 19:52:34
Another way to consider the problem is to remember that the equation is the equivalent of Gauss' Law for Magnetism. Hence, the total magnetic flux through any Gaussian surface must be 0. The only diagram which definitely has a flux through the walls of the box is diagram D. NEC
T
2005-11-08 21:20:01
NEC

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