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

[deepankvora]

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!

 

[espen180]

Current is $$\frac{dQ}{dt}$$, 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.