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battery is connected between point X and y on the circumference of uniform conducting ring of radius a and resistance R, . the smaller arc between X and y substance and angle 60 degree at the centre and magnetic induction at O  due to current in the small arc is 0.1 tesla in outward direction. magnetic induction at O produce current in large arc between X and y is:- 1) 0.6T in the inward direction. 2)0.1T in the inward direction. 3)0.6T in the outward direction. 4)0.1 T in outward direction.
Asked by jhajuhi19 | 25 Apr, 2019, 18:21: PM
answered-by-expert Expert Answer
Let us consider the magnetic field due to current flowing in anticlockwise direction in a
circular arc of radius R and  length L as shown in figure 1.
 
Magnetic field B at centre O is given by Biot-savarts  law ,  B = begin mathsize 12px style integral fraction numerator mu subscript 0 over denominator 4 πR squared end fraction space i space stack d l with rightwards arrow on top space cross times space R with hat on top space equals space fraction numerator begin display style mu subscript 0 space i end style over denominator begin display style 4 πR squared end style end fraction L space end style Tesla 
Hence magnetic field is proportional to arc Length and Current.
If current flows in anti-clockwise direction magnetic field is outward.
If current flows in clockwise direction magnetic field is inward.
 
In Figure.2, if  anti-clockwise direction current flowing in minor arc produces 0.1T magnetic field at O in outward direction,
Magnitude of Magnetic field at O due to clockwise direction current flowing in major arc depends on the product of current and arc length.
 
since arc length of major arc is 5 times of arc length of minor arc, its resistance increases by 5 times ,
 
hence current in major arc becomes (1/5) of current flowing in minor arc. 
Hence the product of ( current × arc Length ) remains same, because current becomes 1/5 and length becomes 5 times.
Hence magnitude of magnetic field will be same.
But due to change in current direction, direction of magnetic field due to major arc is inward.
 
Hence answer to the question :-  (2) 0.1T inward direction
Answered by Thiyagarajan K | 26 Apr, 2019, 10:46: AM

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