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# why magnetic field due to infinitely  long wire and finite long wire comes out to be same using amperes law?

Eshan
3 years ago
Dear student,

If this is so, you are making a mistake while applying the Ampere’s law. Ampere’s law only states that line integral of magnetic field is equal to$\dpi{80} \mu_0 I$, which is always true.

Hence$\dpi{80} \int\vec{B}.d\vec{l}=\mu_0I$is always true.

However if you expanded it to$\dpi{80} \int\vec{B}.d\vec{l}=B(2\pi r)$, you have assumed yourself that magnitude of magnetic field is constant as well as ‘along’ the circular path, which is a wrong assumption. Hence by using you cannot proceed further from$\dpi{80} \int\vec{B}.d\vec{l}=\mu_0 I$, and you would have to use biot-savart’s law.