GREPhysics.NET: GR8677 #79

GR8677 #79

Problem

GREPhysics.NET Official Solution

Electromagnetism $\Rightarrow$ }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 $\nabla \cdot \vec{B}$

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Comments

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). Reply to this comment
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. Reply to this comment
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. Reply to this comment
T 2005-11-08 21:20:01	Reply to this comment

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