Current and electric field strength question

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Homework Help Overview

The problem involves a wire carrying current through three sections with varying radii, prompting a ranking of current, current density, and electric field strength across these sections. The subject area encompasses concepts of electric current, current density, electric fields, and resistance.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to reason through the conservation of charge to determine current distribution across the sections. They also explore relationships between current density and cross-sectional area, while questioning the electric field strength based on intuition.
  • Some participants raise questions about the voltage drop across the sections and seek connections between voltage, area, and resistance.
  • Others suggest considering Ohm's Law and resistivity in relation to the voltage drop.

Discussion Status

Contextual Notes

Participants express uncertainty about the equations needed to relate voltage and area, indicating a potential gap in information or understanding of the underlying principles.

downwithsocks
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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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