The ratio of magnetic field at the centre of circular loop to the magnetic field at the centre of a square loop which are made by a constant length current carrying wire is____

Asked by Areeba Ahmad | 1st Nov, 2014, 11:23: PM

Expert Answer:

 
F o r space c i r c u l a r space l o o p comma L e n g t h space L space equals space 2 πr Magnetic space field space straight B space equals space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction fraction numerator 2 πi over denominator straight r end fraction space equals space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction space fraction numerator 4 straight pi squared straight i over denominator straight r end fraction  For space square space loop comma magnetic space field space at space the space centre space due space to space 4 space sides : Length space straight L space equals space 4 straight a straight B space equals space 4 space cross times space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction fraction numerator 2 square root of 2 straight i over denominator straight a end fraction straight B space equals space space space fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction fraction numerator 8 square root of 2 straight i over denominator open parentheses begin display style 1 half end style πr close parentheses end fraction Hence comma space straight B subscript circular over straight B subscript square equals space space fraction numerator open square brackets fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction space fraction numerator 4 straight pi squared straight i over denominator straight r end fraction close square brackets over denominator open square brackets fraction numerator straight mu subscript straight o over denominator 4 straight pi end fraction fraction numerator 8 square root of 2 straight i over denominator open parentheses begin display style 1 half πr end style close parentheses end fraction close square brackets end fraction equals space fraction numerator straight pi squared over denominator 8 square root of 2 end fraction

Answered by Sheetal Jalan | 2nd Nov, 2014, 12:34: PM