Current and electric field strength question

AI Thread Summary
The discussion centers on a wire carrying current through three sections with varying radii, focusing on the ranking of current, current density, and electric field strength. For current, all sections (A, B, C) must carry the same amount due to charge conservation. Current density is inversely related to the cross-sectional area, leading to the ranking B > C > A. The electric field strength is less clear; intuition suggests A > C > B, but the participant struggles to relate voltage drop to section area without specific resistivity values. Clarification on the relationship between voltage, area, and resistance is sought to resolve the confusion regarding electric field strength.
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Homework Statement


A wire carries a current and consists of three sections with different radii. Rank the sections according to the following quantities, greatest first: (a) current, (b) magnitude of current density, and (c) magnitude of electric field.

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Homework Equations


i = int(J).dA



The Attempt at a Solution


a) A = B = C since charge is conserved and the same amount of current must enter and leave each section. Is this correct?

b) From the given equation, J = i/A. So the cross section with the greatest area will have the lowest current density, thus B > C > A. Correct?

c) Intuition tells me A > C > B but I can't even really convince myself that that's correct let alone explain why with an equation, could anybody help me along?
 
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Which section has the greatest voltage drop? Then use: E=-ΔV/Δx .
 
I'm not sure how to tell which section has the greatest voltage drop...looking in my book I can't find an equation that relates voltage and area..
 
Resistance ? Resistivity ? Ohm's Law ?
 
V = IR? Wouldn't I need a value for the resistivity then?
 
downwithsocks said:
I'm not sure how to tell which section has the greatest voltage drop...looking in my book I can't find an equation that relates voltage and area..

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/resis.html"
 
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