One of Maxwell’s equation is ∇ ∙ B = 0. Which of the following sketches shows magnetic field lines that clearly violate this equation within the region bounded by the dashed lines?
Gauss' law of magnetism, ∇ ∙ B = 0:
- Total magnetic flux through the gaussian surface is zero
- No magnetic monopole
- B is a constant
(A) and (B) show B is a constant.
Net flux is zero (total lines in = out)
TRUE.
(C) shows magnetic field between two different poles.
Net flux is zero (total lines in = out)
TRUE
(D) shows a magnetic monopole, and
Net flux is not zero (0 lines in, 8 out), and
B is not a constant (spread out).
FALSE
(E) shows magnetic field around a straight wire.
Net flux is zero (no line in and out)
TRUE.
Answer: D
(GR8677 #79)
Solution:
Gauss' law of magnetism, ∇ ∙ B = 0:
- Total magnetic flux through the gaussian surface is zero
- No magnetic monopole
- B is a constant
(A) and (B) show B is a constant.
Net flux is zero (total lines in = out)
TRUE.
(C) shows magnetic field between two different poles.
Net flux is zero (total lines in = out)
TRUE
(D) shows a magnetic monopole, and
Net flux is not zero (0 lines in, 8 out), and
B is not a constant (spread out).
FALSE
(E) shows magnetic field around a straight wire.
Net flux is zero (no line in and out)
TRUE.
Answer: D
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