Question

A small bar magnet is placed with its north pole facing magnetic north pole of earth. The neutral points are located at distance $r$ from its centre. If the magent is rotated by 180${}^{\circ }$, netural point shall be obtained at distance

• A. $2r$
• B. $\sqrt{2}r$
• C. $2^{\left(-\frac{1}{3}\right)}r$
• D. $\frac{r}{2\sqrt{2}}$

Answer 1

The correct option is C $2^{\left(-\frac{1}{3}\right)}r$

Neutral point is obtained when horizontal component of earth's magnetic filed is cancelled by the magnetic field of magnet.

Initially the north pole of magnet is directed towards magnetic north of earth. In this case, the netural point can only be obtained on axial location.


Let $\text{P}$ be the neutral point initially.

$B_H=B_{magnet}$

$B_H=\frac{2KM}{r^3}....\left(1\right)$

When, the magent is turned by 180${}^{\circ }$, the neutral point will be obtained strictly for equitorial position. (Let's say at point $\text{Q}$ a distance $r^{\prime }$ from centre)




For neutral point $\text{Q}$

$B_H=B_{magnet}$

$B_H=\frac{KM}{r^{\prime 3}}......\left(2\right)$

From equation $\left(1\right)$ and $\left(2\right)$,

$\frac{KM}{r^{\prime 3}}=\frac{2KM}{r^3}$

$\Rightarrow r^{\prime }=2^{\left(-\frac{1}{3}\right)}r$

Hence, option $\left(C\right)$ is the correct answer.

Why this Question? Tip: Neutral point is a point having zero net magnetic field. In the given scenario, the horizontal component of earth's magnetic field is nullified by the magnetic field of the bar magnet and the neutral point is achieved.