Question

Neutral point is a point where
(A) Magnetic field is zero
(B) Magnetic field is neutral
(C) Neutrality of polarity is present
(D) None of the above

Answer 1

Hint: Consider the horizontal component of the magnetic field of the earth and a magnetic field due to magnet. The neutral point is the point where the magnetic field due to the magnet is equal and opposite to that of the earth.

Complete step by step answer:
- So, the magnetic field at a point due to a magnet and the earth is the vector sum of the individual magnetic fields. Mathematically, the net magnetic field is given by \[\overrightarrow {{B_M}} + \overrightarrow {{B_E}} \].
- For a neutral point, the magnetic field due to a magnet is equal and opposite to that of the earth. Mathematically, $\overrightarrow {{B_M}} = - \overrightarrow {{B_E}} $, this implies that $\overrightarrow {{B_M}} + \overrightarrow {{B_E}} = 0$.
- If a neutral point is to be determined, one can simply put a compass needle at that point. The needle would remain unaffected pointing out in any direction.
Therefore, a neutral point is a point where the magnetic field is zero.

So, the correct answer is “Option A”.

Additional Information:
The neutral point can change its position according to the orientation of the magnet. If the north pole of the magnet is pointing towards the geographical north pole of the earth, there will be two neutral points. Both the neutral points will be located at the equator. If the south pole of the magnet is pointing towards the geographical north pole of the earth, in this case also there will be two neutral points and both will be located on its axial line or the axis of the magnet. Here we can see that, if the magnet is rotated by an angle of $180^\circ $, corresponding to the rotation the neutral point changes its position by an angle of $90^\circ $. In general, you can say that if the magnet is rotated by an angle of $\theta $, the neutral point will change its position at an angle of $\dfrac{\theta }{2}$.

Note:
- The point to be noted is that, here the magnetic field of the earth is actually the horizontal component of the earth’s magnetic field.
- In case when the north pole of the magnet is pointing towards the geographical north pole of the earth, the magnetic field of the magnet at the neutral point will be $B = \dfrac{{{\mu _0}}}{{4\pi }}\dfrac{M}{{{{\left( {{d^2} + {l^2}} \right)}^{\dfrac{3}{2}}}}}$.
- In case when the south pole of the magnet is pointing towards the geographical north pole of the earth, the magnetic field of the magnet at the neutral point will be $B = \dfrac{{{\mu _0}}}{{4\pi }}\dfrac{{2Md}}{{{{\left( {{d^2} - {l^2}} \right)}^2}}}$.