Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moment \overrightarrow m . Which configuration has highest net magnetic dipole moment ?

Magnetism and Matter question

2014 · Q126

2014 · Q126

View written solutionFree

Correct answer: C

In configuration (1),

m_net =

\sqrt {{m^2} + {m^2} + 2mm\cos 90^\circ }

=

\sqrt {{m^2} + {m^2}} = 2\sqrt m

In configuration (2),

m_net = m - m = 0

In configuration (3),

m_net =

\sqrt {{m^2} + {m^2} + 2mm\cos 30^\circ }

=

\sqrt {2{m^2} + 2{m^2}\left( {{{\sqrt 3 } \over 2}} \right)}

=

m\sqrt {2 + \sqrt 3 }

In configuration (4),

m_net =

\sqrt {{m^2} + {m^2} + 2mm\cos 30^\circ }

=

\sqrt {2{m^2} + 2{m^2}\left( {{1 \over 2}} \right)} = m\sqrt 3

2014 · Q126

2014 · Q126

View written solutionFree

Correct answer: C

In configuration (1),

m_net =

\sqrt {{m^2} + {m^2} + 2mm\cos 90^\circ }

=

\sqrt {{m^2} + {m^2}} = 2\sqrt m

In configuration (2),

m_net = m - m = 0

In configuration (3),

m_net =

\sqrt {{m^2} + {m^2} + 2mm\cos 30^\circ }

=

\sqrt {2{m^2} + 2{m^2}\left( {{{\sqrt 3 } \over 2}} \right)}

=

m\sqrt {2 + \sqrt 3 }

In configuration (4),

m_net =

\sqrt {{m^2} + {m^2} + 2mm\cos 30^\circ }

=

\sqrt {2{m^2} + 2{m^2}\left( {{1 \over 2}} \right)} = m\sqrt 3