Distribution of current in a conductive plate

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Discussion Overview

The discussion revolves around the distribution of current in a conductive plate within a circuit, specifically how the current varies across the plate and methods to measure it. The scope includes theoretical considerations of current density, practical measurement techniques, and the impact of circuit components on current flow.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant suggests that the current through the plate would decrease as one moves away from the axis of the wire, but questions the specific manner of this decrease.
  • Another participant proposes that the current density distribution will be complex, indicating that the current exiting the wire spreads out and then converges before entering the other wire, with the distribution minimizing the net resistance of the plate. They note that the solution may depend on geometry and resistivity, and express uncertainty about the existence of an analytic solution.
  • A participant inquires about the feasibility of measuring current in a small section of the plate using an ammeter, questioning whether touching the leads a small distance apart would work.
  • Another participant responds that using an ammeter would significantly alter the current flow due to its low resistance, but suggests that using a voltmeter with closely spaced needles could provide a good estimate of current flow by applying the resistivity of the metal.

Areas of Agreement / Disagreement

Participants express differing views on the complexity of current distribution and measurement techniques, indicating that there is no consensus on the exact behavior of current within the plate or the best method for measurement.

Contextual Notes

There are limitations regarding the assumptions about the geometry of the plate and the resistivity of the material, as well as the potential impact of measurement tools on current flow.

Who May Find This Useful

Individuals interested in circuit theory, electrical engineering, and experimental physics may find this discussion relevant.

papernuke
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There's a circuit with voltage source V resistance R and current i.
One section of the circuit has a conductive 'plate' element, connected like this:

-----wire-------metal plate------wire----rest of circuit

How does the current through the plate vary within the plate? I'm fairly certain the current would decrease as you moved up or down away from the axis of the wire, but decrease in what manner?
 
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The current density distribution is actually going to be quite complex. The current exiting the wire would spread out, and then bunch up together before entering the other wire. The total distribution is such that it minimizes the net resistance of the metal plate. Solution will depend on geometry and resistivity of the plate. And I'm not sure if there is an analytic solution or if you have to do this one numerically.
 
Is there a way to physically determine current in a small section of the plate? Would it work to simply to touch the leads of ammeter to the plate, a small distance apart?
 
Nope. You'd alter the current flow dramatically if you do that because ammeter has very low resistance. But if you touch the needles of a voltmeter very close together on the plate, you can get a good estimate of the current flow between these two points by using the resistivity of the metal in question.
 
Oh, right
Thanks for the help!
 

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