 # The Maxwell equation derived from Gauss's Law in magnetism is a)oint vec(B) vec(ds)=mu_0 I+ epsilon_0 mu_0 (d Phi_E)/(dt) b)oint vec(B) vec(dA)=0 c)oint vec(E) vec(dA)=(Q_(in))/(epsilon_0) d)oint vec(E) vec(ds)=-(d Phi_m)/(dt) Lilliana Livingston 2022-07-20 Answered
The Maxwell equation derived from Gauss's Law in magnetism is
a) $\oint \stackrel{\to }{B}\stackrel{\to }{ds}={\mu }_{0}I+{ϵ}_{0}{\mu }_{0}\frac{d{\mathrm{\Phi }}_{E}}{dt}$
b) $\oint \stackrel{\to }{B}\stackrel{\to }{dA}=0$
c) $\oint \stackrel{\to }{E}\stackrel{\to }{dA}=\frac{{Q}_{in}}{{ϵ}_{0}}$
d) $\oint \stackrel{\to }{E}\stackrel{\to }{ds}=-\frac{d{\mathrm{\Phi }}_{m}}{dt}$
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According to Gausss law for magnetism the net magnetic flux through any closed surface is zero
So, $\mathrm{\Phi }=\oint d\varphi =\oint \stackrel{\to }{B}\cdot d\stackrel{\to }{A}=0$
where, $\varphi$=magnetic flux
B=magnetic field
dA= area element
Hence option b is correct
option (a) is incorrect because it is ampere maxwell law
option (c) is incorrect because it is Gausss law for electricity and option (d) is also incorrect because it is faraday`s law