長直導線所產生的磁場的推導

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We can use the Biot Law to find the expression.

Now, we use the Biot Law to find out the magnetic field B at point P due to an infinity long straight conducting wire carrying a current I.

Let r represent the radial distance of point P from the wire and s the vector from a current element to P. Then, by the Biot law,


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where k' = μ0/4π

This is a vector integral, but since the field dB set up at P by any other element of the conductor is parallel to the vector dB in the diagram, the resultant field is the algebraic sum or the sum of the magnitudes dB. Then since s^ is a unit vector,


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