The resultant magnetic moment of three magnetic dipoles,each of magnetic moment $M$,shown in the arrangement is:

  • A
    $\sqrt{2} M$
  • B
    $(\sqrt{2}+1) M$
  • C
    $(\sqrt{2}-1) M$
  • D
    $M$

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$A$ magnetised wire of magnetic moment $M$ is bent into an arc of a circle subtending an angle of $60^{\circ}$ at the center. The new magnetic moment is:

Two identical thin bar magnets,each of length $l$ and pole strength $m$,are placed at a right angle to each other with the north pole of one touching the south pole of the other. The magnetic moment of the system is

Two equal bar magnets are kept as shown in the figure. The direction of the resultant magnetic field,indicated by the arrow head at the point $P$,is (approximately):

Use:
$(i)$ the Ampere's law for $\vec{H}$ and
$(ii)$ continuity of lines of $\vec{B}$,to conclude that inside a bar magnet,
$(a)$ lines of $\vec{H}$ run from the $N$ pole to $S$ pole,while
$(b)$ lines of $\vec{B}$ must run from the $S$ pole to $N$ pole.

Magnetic lines of force due to a bar magnet do not intersect because

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