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Asked by ntg432000 | 30 Mar, 2019, 22:03: PM
answered-by-expert Expert Answer
Magnetic field B at the centre of arc is obtained by integrating Biot-Savart's law
 
that is applied to segment legth dl along the length of arc 
 
B = begin mathsize 12px style integral d B space equals integral space fraction numerator mu subscript o i over denominator 4 straight pi end fraction cross times fraction numerator stack d l with rightwards arrow on top space cross times space r with hat on top over denominator r squared end fraction space space equals space fraction numerator mu subscript o i over denominator 4 straight pi space straight r squared end fraction space integral d l end style
at each point of arc length segment dl and unit vector along radial direction are perpendicular. 
cross product of vectors equals segment length dl
Hence by keeping all parameters constants, integration of length segment becomes length of arc, i.e. (π/2)r .
 
Hence Magnetic field B = begin mathsize 12px style fraction numerator mu subscript o space i over denominator 4 straight pi space straight r squared end fraction cross times πr over 2 space equals space fraction numerator mu subscript o space i over denominator 8 space r end fraction space T e s l a end style
Answered by Thiyagarajan K | 31 Mar, 2019, 10:41: AM

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