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Question
Use this law to find magnetic field due to straight infinite current carrying wire.
Solution
Magnetic field due to straight infinite current carrying wire:
The figure below shows a straight infinite current carrying wire around which a circular loop of radius r is shown
The field lines are circular, and hence, the field B at any point of the circular loop is directed along the tangent to the circle at that point. The magnitude of field B is the same at every point of the circular loop.
Therefore, we get
∫B.dl=∫Bdl cosθ = ∫Bdl cos0 = B∫dl =B(2πr)
Now, from Ampere’s circuital law, the above equation is
`B(2pir)=mu_0I`
`:.B=(mu_0I)/(2pir)`
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