Question

A long, vertical wire carrying a current of 10 A in the upward direction is placed in a region where a horizontal magnetic field of magnitude 2.0 × 10⁻³ T exists from south to north. Find the point where the resultant magnetic field is zero.

Answer 1

Given:
Uniform magnetic field, B₀ = 2.0 × 10⁻³ T (From south to north)
To make the resultant magnetic field zero, the magnetic field due to the wire should be of the same magnitude as B₀ and in the direction north to south.
The above condition will be satisfied when the required point will be placed in the west w.r.t. the wire.
Let the separation of the point from the wire be d.

The magnetic field due to current in the wire is given by
$B=\frac{{\mu }_{0}I}{2\pi d}$

From the question, B = B₀.
$\Rightarrow 2.0\times {10}^{-3}=\frac{{\mu }_{0}I}{2\mathrm{\pi }d}$
$$\begin{gathered} \Rightarrow 2.0\times {10}^{-3}=\frac{2\times {10}^{-7}\times 10}{d} \\ \Rightarrow d={10}^{-3}\mathrm{m}=1\mathrm{mm} \end{gathered}$$