Ampere's circuital law on finite length wire

AI Thread Summary
Applying Ampere's circuital law to a finite length wire yields incorrect results due to the accumulation of charge, indicating that the current may not be steady. While Biot-Savart's law is also applicable only to steady currents, it can be used to calculate the magnetic field of a finite segment of wire, although it typically requires a closed loop for complete analysis. The discussion highlights that a steady current can exist in a finite wire, particularly in DC circuits, but challenges arise when the wire is not part of a closed loop. The calculation of magnetic fields from finite wires involves considering contributions from segments of the wire and potentially multiplying results for symmetry. Overall, the complexities of applying these laws to finite wires prompt further exploration and clarification in the context of magnetic field calculations.
s.gautam
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When we apply ampere's circuital law to finite length wire,we get the wrong answer.Why is that? The symmetry rule is being followed,so that's not the problem.
Is it because a finite length wire means that charge is piling up somewhere which means that the current is not steady?
 
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Thanks a lot,that was really helpful.
 
s.gautam said:
Thanks a lot,that was really helpful.
Pleasure :biggrin: Welcome to the forums!
 
Hey another thought occurred to me,how can we apply biot-savart's law to determine the magnetic field of a finite length wire? Biot-savart's law is also valid for only steady currents.
 
I guess I should post it in a new thread.
 
s.gautam said:
Hey another thought occurred to me,how can we apply biot-savart's law to determine the magnetic field of a finite length wire? Biot-savart's law is also valid for only steady currents.

A wire of finite length can have a steady current, same as a wire of infinite length. Indeed this is precisely the case in any DC circuit.
 
Yes,it can,but not until its in a closed loop.With biot-savart law,we find out the field of a finite segment of wire which is not a closed loop,and this is what's troubling me.
 
You're right, it does need to be in a closed loop, but what we can do when we calculate it, is calculate the contribution to the magnetic field of the finite straight wire. It is still left to calculate the field of the rest of the loop. If you're working out of griffith's 2nd ed. See for example Problem 5.37, where you calculate the contribution from one side of the square then multiply it by four.
 

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