Question

Two like magnetic poles of strength $10$ and $40$ Am are separated by a distance $30cm$ . The intensity of magnetic field is Zero on the line joining them.
A. At a point $10cm$ from a stronger pole
B. At a point $20cm$ from a stronger pole
C. At a mid-point
D. At infinity

Answer 1

Hint:
This problem is based on the intensity of the magnetic field and we know that if the magnetic field (B) at any point is zero, then the intensity of magnetic field (H) at that point will also be zero due as $B = \mu H$ hence, use the relation $B = \dfrac{{{\mu _o}}}{{4\pi }}\dfrac{m}{{{d^2}}}$to get an accurate solution to the given problem.

Formula used:
The formula used in this solution is given as: -
$B = \dfrac{{{\mu _o}}}{{4\pi }}\dfrac{m}{{{d^2}}}$



Complete step by step solution:
We know that the Magnetic Induction at a point in a magnetic field is given as: -
$B = \dfrac{{{\mu _o}}}{{4\pi }}\dfrac{m}{{{d^2}}}$ … (1)
The given problem can be illustrated by a diagram given as follows: -


Let us consider that the magnetic field is zero at a point P which lies $x$cm from magnet A (10 units) and $(x - 30)$cm from magnet B (40 units).
So, From eq. (1)
$\therefore \dfrac{{{\mu _o}}}{{4\pi }}\dfrac{{\left( {10} \right)}}{{{x^2}}} = \dfrac{{{\mu _o}}}{{4\pi }}\dfrac{{\left( {40} \right)}}{{{{\left( {30 - x} \right)}^2}}}$
$ \Rightarrow \dfrac{{{{\left( {30 - x} \right)}^2}}}{{{x^2}}} = 4$
On further Calculation, we get a quadratic equation as: -
$ \Rightarrow 900 + {x^2} - 60x = 4{x^2}$
$ \Rightarrow 3{x^2} + 60x - 900 = 0$
On Solving this equation, we get
$ \Rightarrow x = 10cm$
i.e., the distance of magnet A (10 units) from point P = $x = 10cm$
and the distance of magnet B (40 units) from point P = $30 - x = 30 - 10 = 20cm$
As, the stronger magnetic pole is B and the magnetic field is zero at a point $20cm$ from a stronger pole. Thus, the intensity of magnetic field is also zero on the line joining the magnets at a point $20cm$ from a stronger pole.
Hence, the correct option is (B) At a point $20cm$ from a stronger pole.



Therefore, the correct option is B.




Note:
 A particular point at which resultant magnetic field intensity is zero due to earth’s magnetic field is called a neutral point. Or in other word a null point is that particular point where the magnetic field is completely neutralised by the horizontal component of the magnetic field of earth.