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The current density equation states that $J = I/A$.

But I got a question that asking the current density over an infinite plate. Say the current $I_0$ flows into the infinite plate that extent infinitely on $z$ direction from $x = 0$ to $d$, What's the current density on the plate? The plate in unspecified on $y$.

I have asked a professor regarding this, and the answer is $J = I$. I have trouble to understand why infinite count as 1 in this case. Could anyone sent some help?

Thanks in advance.

edit:

Here is the question, question (a). enter image description here

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  • $\begingroup$ Related: Surface current density confusion $\endgroup$
    – G. Smith
    Commented Aug 21, 2020 at 23:04
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    $\begingroup$ I have asked a professor regarding this, and the answer is J = I. Don’t ask that professor any more questions about EM. $\endgroup$
    – G. Smith
    Commented Aug 21, 2020 at 23:05
  • $\begingroup$ Thank you for your reply. .I still don`t get the answer. How can I write the current density? $\endgroup$
    – Chtholly
    Commented Aug 21, 2020 at 23:59
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    $\begingroup$ It seems to me that it’s zero times a delta function. The situation you have described is sufficiently strange than I am skeptical it is really what the problem asked. Can you please edit your question to quote the problem exactly as it is stated? $\endgroup$
    – G. Smith
    Commented Aug 22, 2020 at 0:20
  • $\begingroup$ I have added the original question. I think those problems are pretty straightforward except (a). Maybe I have a misunderstanding here. $\endgroup$
    – Chtholly
    Commented Aug 22, 2020 at 0:37

1 Answer 1

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The question is given in a rather vague language. The interpretation that the question is demanding is probably the following:

Instead of thinking about I as the total current that is spreading in the infinite area , you could imagine I being supplied to each unit strip where the strips are taken perpendicular to the $x-z$ plane.That is to mean that the source is providing I to all such strips extending in the $y$ direction and hence the net current through the whole sheet is infinite while current density is I itself.

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  • $\begingroup$ If that`s the case, then (b),(c) and(d) would become infinite. $\endgroup$
    – Chtholly
    Commented Aug 22, 2020 at 18:10
  • $\begingroup$ Yes. You are right , I didn't even look at the other sub-parts. You might have to consider what G.Smith has said. Maybe the question is requiring to neglect the infinite extension. $\endgroup$
    – Lost
    Commented Aug 22, 2020 at 18:27

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