Question

A current of $5A$ flows downwards in a long straight conductor.The earth's horizontal flux density is $2\times {10}^{-7}T.$ The neutral point is:

• A. due north $10m$ from the wire
• B. due east $10m$ from the wire
• C. due east $5m$ from the wire
• D. due west $5m$ from the wire

Answer 1

The correct option is C due east $5m$ from the wire

magnetic field due to infinite wire $=\frac{{\mu }_{0}i}{2\pi r}$
at neutral point , net magnetic field $=0$
so magnetic field due to wire = magnetic field due to earth
$\frac{{\mu }_{0}5}{2\pi x}=2\times {10}^{-7}$
this gives $r=5m$
It will be due east because in the east direction , magnetic field lines due to wire will be running against the magnetic field due to earth so both will cancel each other