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

Options

A. `sqrt(2) M`
B. `(sqrt(2 )+ 1)` M
C. `(sqrt(2 )- 1)` M
D. M

Answer

B

Explanation

Three magnetic moments of magnetic dipole, are shown in the figure below as,

Here, `M_(1) = sqrt(M_(A)^(2) + M_(B)^(2) + 2M_(A)M_(B) cos 90^(@))`
`rArr M_(1) = sqrt(M^(2) + M^(2) + 0)`
`rArr M_(1) = Msqrt(2)`
Now, the resultant, magnetic moment,
`M_("resultant") = M_(1) + M_(C )`
(`because M_(1)` and `M_(C )` are in the same direction)
`rArr M_("resultant") = Msqrt(2) + M`
`rArr M_(resultant") = (1+sqrt(2)) M`
`:.` correct option is (b).