Why Does the Same Current Flow Through Every Segment of a Wire?

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The discussion clarifies that the current 'i' flowing through a wire remains constant across all segments, as established by fundamental principles of electric current. The user initially questioned why a small element of the wire, denoted as 'dl', should also have the same current 'i' instead of a different value 'di'. The explanation provided emphasizes that current is defined as the rate of charge flow, i = dQ/dt, which does not vary with the length of the wire segment. Additionally, any variation in current would lead to charge accumulation, contradicting Kirchhoff's junction rule.

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Curent Electricity Doubt! PLEASE HELP!

Homework Statement


I did not understand one thing.. If it is given that a wire has a current 'i', then why do we say (in applications of laws such as biot savart law) that the current in a small element of the wire is also 'i', that is the same current that passes through the whole conductor.


Homework Equations


can someone explain this. i got really confused on this one.


The Attempt at a Solution


I thought we should take current in the ' dl ' element of the wire as ' di ' and not i. I am wrong. Please Explain, anyone!
 
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Current is [tex]\frac{dQ}{dt}[/tex], the amount of charge which passes through a cross-section of the wire per unit time. This value does not depend on the length segment of wire.

Also, for one segment of wire to have a different current than another causes a buildup of charge, inconsistent with Kirchhoff's junction rule.
 

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