Question
Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moment $$M.$$ Which configuration has highest net magnetic dipole moment?
Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moment $$M.$$ Which configuration has highest net magnetic dipole moment?
A.
(i)
B.
(ii)
C.
(iii)
D.
(iv)
Answer :
(iii)
Solution :
Magnetic moment is from $$S$$ to $$N$$
So, $${M_{{\text{net}}}} = \sqrt {{M^2} + {M^2} + 2{M^2}\cos \theta } $$
$${M_{{\text{net}}}}$$ will be maximum if $${\cos \theta }$$ is maximum. $${\cos \theta }$$ will be maximum when $$\theta $$ will be minimum.
So, at $$\theta = {30^ \circ },{M_{{\text{net}}}}$$ will be maximum.
Magnetic moment is from $$S$$ to $$N$$
So, $${M_{{\text{net}}}} = \sqrt {{M^2} + {M^2} + 2{M^2}\cos \theta } $$
$${M_{{\text{net}}}}$$ will be maximum if $${\cos \theta }$$ is maximum. $${\cos \theta }$$ will be maximum when $$\theta $$ will be minimum.
So, at $$\theta = {30^ \circ },{M_{{\text{net}}}}$$ will be maximum.