Physics-
General
Easy

Question

Two short bar magnets of equal dipole moment M are fastened perpendicularly at their centers, figure. The magnitude of resultant of two magnetic field at a distance d from the center on the bisector of the right angle is

  1. fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 2 square root of 2 M over denominator d to the power of 3 end exponent end fraction    
  2. fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 2 M over denominator d to the power of 3 end exponent end fraction    
  3. fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator M over denominator d to the power of 3 end exponent end fraction    
  4. fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 2 square root of 2 M over denominator d to the power of 3 end exponent end fraction    

The correct answer is: fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 2 square root of 2 M over denominator d to the power of 3 end exponent end fraction


    Resolving the magnetic moments along O P and perpendicular toO P comma figure we find that component O P perpendicular O P cancel out. Resultant magnetic moment along O P i s equals M cos invisible function application 45 degree plus M c o s 45 degree

    equals 2 blank M c o s blank 45 degree equals fraction numerator 2 M over denominator square root of 2 end fraction equals square root of 2 M
    The point P lies on axial line of magnet of moment
    equals square root of 2 M
    therefore B equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator 2 left parenthesis square root of 2 M right parenthesis over denominator d to the power of 3 end exponent end fraction

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