A magnet placed in the magnetic meridian with its north pole pointing north of the earth produces a neutral point at a distance of `0*15m` from either pole. It is then broken into two equal parts and one such piece is placed in a similar position. Find the position of the neutral point.

Explanation

As N-pole of magnet is pointing north, neutral points lie on equatorial line of magnet at a distance x from each pole.
`:. H=B_(eqn.)=(mu_0)/(4pi)(M)/(x^3)` …(i)
When the magnet is broken into two equal parts, pole strength remains unchanged, but magnetic moment is reduced to half
i.e., `M^'=M//2`
If `x^'` is distance of neutral point from each pole of the part, then
`H=(mu_0)/(4pi)xx(M^')/(x^('3))` ...(ii)
From (i) and (ii),
`(mu_0)/(4pi)(M^')/(x^('3))=(mu_0)/(4p)(M)/(x^3)`
`x^('3)=x^3M^'/M=x^3/2`
`x^'=(x)/(2^(1//3))=(0*15)/(1*26)=0*119m` from each pole