The formula to calculate the magnitude of the magnetic field at a distance d on the axis of the magnet is,
B 1 = μ 0 4π ( 2m d 1 3 )
Here, the permeability of the free space is μ 0 , the magnetic moment is m, the magnitude of the magnetic field is B 1 and the distance from the bar magnet is d.
If the bar magnet is turned by 180°, then the neutral point will lie on the equatorial line.
The formula to calculate the magnitude of the magnetic field at a distance d on the equatorial line of a magnet is,
B 2 = μ 0 4π ( m d 2 3 )
The magnetic field in both cases are equal so the formation of the equation is,
μ 0 4π ( 2m d 1 3 )= μ 0 4π ( m d 2 3 ) 2 d 1 3 = 1 d 2 3 ( d 2 d 1 ) 3 = 1 2 d 2 = d 1 ( 1 2 ) 1 3
Substituting the values in the above equation, we get:
d 2 =( 14 ) ( 1 2 ) 1 3 ≈11.1 cm
Thus, the new null point is located at 11.1 cm on the normal bisector.