What’s the current density on infinite plate?

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?

edit:

Here is the question, question (a).

• Commented Aug 21, 2020 at 23:04
• I have asked a professor regarding this, and the answer is J = I. Don’t ask that professor any more questions about EM. Commented Aug 21, 2020 at 23:05
• Thank you for your reply. .I still dont get the answer. How can I write the current density? Commented Aug 21, 2020 at 23:59
• 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? Commented Aug 22, 2020 at 0:20
• I have added the original question. I think those problems are pretty straightforward except (a). Maybe I have a misunderstanding here. Commented Aug 22, 2020 at 0:37

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.