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I What does Griffith mean by this hint? [Electrodynamics]

  1. Apr 26, 2017 #1
    I was solving the problems given by Griffith in his book 'Introduction to Electrodynamics' and stumbled across this question.
    Screenshot_3.png Screenshot_12.png
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    "Because sigma (conductivity of the medium) is a function of position, the equation 7.5 does not hold" --i get this point; current density isn't constant and so its divergence will be non zero.
    "The charge density is non zero in the resistive medium"-- I have no clue what this sentence means.. I can't even think why i don't find it right.. someone please explain it to me!!

    Thanks a lot !
     
  2. jcsd
  3. Apr 26, 2017 #2

    vanhees71

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    2016 Award

    Another hint: Use the constitutive equation
    $$\vec{j}=\sigma \vec{E}$$
    and the continuity equation for stationary currents
    $$\vec{\nabla} \cdot \vec{j}=0,$$
    which together immediately tell you, how to modify Eq. (7.5). Also it would be helpful to tell, what ##s## is. Is it the cylinder coordinate ##r## in standard notation? I guess so from the Figure, which indicates that ##\vec{E}## is radially out.

    PS: Questions like this should be posted in the homework forum!
     
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