As we know, the magnetic field at a distance $r$ from a long wire carrying a current $I$ is given by $ B=\frac{ \mu_0 I}{2 \pi r} $. My question is why it is assumed that the wire is long (infinite)?
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see https://physics.stackexchange.com/questions/14078/using-amperes-circuital-law-for-an-infinitely-long-wire-wire-of-given-length?rq=1 – ProfRob Dec 15 '17 at 15:07
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The assumption of an infinitely long wire makes things simpler, since you know that the magnetic field is symmetric along the wire. The formula for the magnetic field which you stated, can then be obtained by applying Stoke's theorem to Ampère's law.
If the wire is finite the magnetic field will deviate from your simple formula, particularly near the end of the wire. To calculate the field of a finite wire you could use the Biot-Savart law.
ggg
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