A bar magnet of magnetic moment Mis placed at a distance D with its axis along positive X-axis. Likewise, second bar manget of magnetic moment M is placed at a distance 2D on positive Y-axis and perpendicular to it as shown in the figure. The magnitude of magnetic field at the origin  is `|B|=alpha[(eta_(0))/(4pi)(M)/(D^(3))]`. The value of a must be (assume `D gt gt l`, where l is the length of magnets)
 

Options

A. 2
B. `(15)/(8)`
C. `(17)/(8)`
D. `(9)/(8)`

Answer

B

Explanation

Magnetic field at axial point `(d gt gt l)`
`B_(1)=(2mu_(0)M)/(4pi d^(3))" "("from S to N")`
`=(2mu_(0)M)/(4pi D^(3))" "(d=D)`
Magnetic field at equatorial line `(d gt gt l)`
`B_(2)=(2mu_(0)M)/(4pi d^(3))" "("from N to S")`
Now, for equatorial point d = 2D
`:." "B_(2)=(1)/(8)(mu_(0)M)/(4pi D^(3))" "("from N to S")`
So, resultant magnetic field,
`B=B_(1)-B_(2)" "("from S to N")`
`=(mu_(0)M)/(4pi D^(3))(2-(1)/(8))`
`B=(15)/(8)(mu_(0)M)/(4 pi D^(3))" "("in maggnitude")`
On comparing with given formula, we get
`alpha=15//8`