Two short bar magnets are taken and fastened together perpendicularly by their centres as shown in figure. Magnetic moment of each magnet is M and A is a point on bisector of this system at a distance d from the centre as N A S shown in figure. Magnetic field intensity at point A is

Options

A. `B = (mu_0)/(4pi) (M)/(d^3)`
B. `B = (mu_0)/(4pi) (2M)/(d^3)`
C. `B = (mu_0)/(4pi) (M sqrt2)/(d^3)`
D. `B = (mu_0)/(4pi) (2 sqrt2M)/(d^3)`

Answer

D

Explanation

Resultant magnetic moment of this system is `Msqrt2` and is directed along the angle bisector of the system and point A lies on this line. Hence we can assume that it is one magnet of magnetic moment `M sqrt2` and point A lies on its axis at a distance d from the centre. So magnetic field strength on the axis of short magnet can be written as follows:
` B = (mu_0)/(4pi) (2 (M sqrt2) )/(d^3)`
` rArr B = (mu_0)/(4pi) (2 sqrt2 M)/(d^3)`