Question

05. Two N poles of strengths 36 and 64 Am are placed at a distance 20
cm apart. The field is zero at a distance of_ cm from weaker pole.​

Answer 1

Given:

The magnitude of electric current of the first pole, I₁= 36Am

The magnitude of electric current of the second pole, I₂= 64Am

The distance between two poles = 20cm

To FInd:

We have to find the distance from the weaker pole where the magnetic field is neutral.

Solution:

The equation for the magnetic field is given by,

                        $\[B = \frac{{{\mu _0} \times I}}{{4\pi \times {d^2}}}\]$

Let B₁ be the magnetic field of the first pole, then

                       $\[{B_1} = \frac{{{\mu _0} \times 36}}{{4\pi \times {d^2}}}\]$

Let B₂ be the magnetic field of the second pole, then

                       $\[{B_2} = \frac{{{\mu _0} \times 64}}{{4\pi \times {{\left( {20 - d} \right)}^2}}}\]$

It is given that the field is 0, which means B₁ = B₂

                       $\[\begin{gathered} \frac{{36}}{{{d^2}}} = \frac{{64}}{{{{\left( {20 - d} \right)}^2}}} \hfill \\ \frac{6}{d} = \frac{8}{{20 - d}} \hfill \\ \end{gathered} \]$

                      $\[\begin{gathered} 120 - 6d = 8d \hfill \\ 120 = 14d \hfill \\ d = 8 \cdot 57\,cm \hfill \\ \end{gathered} \]$

∴ The field is zero at a distance of 8.57cm from the weaker pole.