A long, vertical wire carrying a current of 10A in the upward direction is placed in a region where a horizontal magnetic field of magnitude  2⋅0×10−3T exists from south to north. Find the point (west to the wire in mm) where the resultant magnetic field is zero.

# A long, vertical wire carrying a current of 10A in the upward direction is placed in a region where a horizontal magnetic field of magnitude  $2\cdot 0×{10}^{-3}\mathrm{T}$ exists from south to north. Find the point (west to the wire in mm) where the resultant magnetic field is zero.

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### Solution:

To cancel the magnetic field the point should be chosen so that the net magnetic field is along - $\stackrel{^}{\mathrm{J}}$  direction
$\therefore$The point is along -$\stackrel{^}{\mathrm{i}}$  direction or along west of the wire $\mathrm{B}=\frac{{\mathrm{\mu }}_{0}\mathrm{i}}{2\pi r}$
$⇒2×{10}^{-3}=\frac{4\mathrm{\pi }×{10}^{-7}×10}{2\mathrm{\pi }×\mathrm{r}}⇒\mathrm{r}=\frac{2×{10}^{-7}×10}{2×{10}^{-3}}={10}^{-3}\mathrm{m}=1\mathrm{mm}$

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