Two identical bar magnets of magnetic moment M each, are placed along X and Y-axes, respectively at a distance d from the origin (as shown in the figure). The origin lies on perpendicular bisector of magnet placed on
X-axis and on the magnetic axis of magnet placed on Y-axis If the magnitude of total magnetic field at the origin is B `= alpha[(mu_(0))/(4pi) (M)/(d^(3))]` then the value of constant `alpha` will be (`d gt gt l.` where lis the lenght of the bar magnets and direction of N to S in magnets is oppsite with respect to each other)

Options

A. 2
B. 1
C. 3
D. `sqrt(5)`

Answer

C

Explanation

Magnetic field due to axial magnet,
`B_(1)=(mu_(0))/(4pi)(M)/(d^(3))` (+ Y direction)
Magnetic field due to equatorial magnet,
`B_(2)= (mu_(0))/(4pi)(M)/(d^(3))` (+ Y direction)
So, effective magnetic field
`B=B_(1)+ B_(2)= 3 (mu_(0)M)/(4pid^(3))`
`rArr alpha=3`