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magnetic effect of current

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Asked by mc8may | 18 Jul, 2023, 10:21: PM

Expert Answer

The view of x-z plane of the given configuration of current carrying wire is shown above.

Let us consider a small element of length dz at distance z from mid point of wire-A₂ .

Magnetic field B due to current rhrough wire-A₁ at the location of dl is

begin mathsize 14px style B space equals space fraction numerator mu subscript o I over denominator 2 straight pi end fraction fraction numerator 1 over denominator square root of z squared plus 3 end root end fraction end style

Magnitude of

begin mathsize 14px style integral B times d z end style

is calculated as follows

begin mathsize 14px style integral B times d z space equals space fraction numerator mu subscript o I over denominator 2 straight pi end fraction integral subscript negative square root of 3 end subscript superscript plus square root of 3 end superscript fraction numerator d z over denominator square root of z squared plus 3 end root end fraction end style

=

begin mathsize 14px style fraction numerator mu subscript o I over denominator 2 pi end fraction space ln left parenthesis space 3 space plus space 2 square root of 2 space right parenthesis end style

Answered by Thiyagarajan K | 19 Jul, 2023, 11:00: AM

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