Two short magnets P and Q are placed one over the other with their magnetic axis mutually perpendicular to each other. it is found that the resultant field at a point on the prolongation of the magnetic field of P is inclined at 30 with this axis. compare the magnetic moments of the two magnets.

Asked by modi72879 | 25th Nov, 2017, 11:35: AM

Expert Answer:

Two short magnets P and Q are placed one over the other with their magnetic axis mutually perpendicular to each other. it is found that the resultant field at a point on the prolongation of the magnetic field of P is inclined at 30 with this axis. compare the magnetic moments of the two magnets.
 
Solution :
 
By using the Biot Savart Law,
 
begin mathsize 12px style straight B subscript 1 equals fraction numerator straight mu subscript 0 over denominator 4 straight pi end fraction. space fraction numerator 2 straight m subscript 1 over denominator straight r cubed end fraction
straight B subscript 2 equals fraction numerator straight mu subscript 0 over denominator 4 straight pi end fraction. space straight m subscript 2 over straight r cubed
Thus comma
straight B subscript 2 over straight B subscript 1 equals fraction numerator straight m subscript 2 over denominator 2 straight m subscript 1 end fraction

Also comma
straight B subscript 2 over straight B subscript 1 equals tan space straight theta
tan space straight theta equals space tan space 30 space... left parenthesis given right parenthesis
tan space 30 space equals fraction numerator 1 over denominator square root of 3 end fraction
So comma
fraction numerator straight m subscript 2 over denominator 2 straight m subscript 1 end fraction equals fraction numerator 1 over denominator square root of 3 end fraction

Which space finally space explains space that comma
straight m subscript 1 over straight m subscript 2 equals fraction numerator square root of 3 over denominator 2 end fraction

end style

Answered by Abhijeet Mishra | 25th Nov, 2017, 11:43: PM