Magnetic Field Due To A Straight Conductor

A long straight current-carrying conductor produces a magnetic field whose lines form concentric circles around the wire, and Ampere's circuital law gives the magnitude as $B=\frac{{\mu }_{0}I}{2\pi r}$. Here the field depends directly on the current and inversely on the perpendicular distance from the wire. Substituting ${\mu }_0=4\pi \times 10^{-7}{\text{T m A}}^{-1}$, $I=10\text{A}$ and $r=0.05\text{m}$, we get $B=\frac{(4\pi \times 10^{-7})(10)}{2\pi (0.05)}=\frac{2\times 10^{-6}}{0.05}=4\times 10^{-5}\text{T}$. The option $2\times 10^{-5}\text{T}$ wrongly uses twice the distance, $10\text{cm}$. The option $1\times 10^{-5}\text{T}$ corresponds to a current of $2.5\text{A}$, not the given value. The option $8\times 10^{-5}\text{T}$ doubles the correct current and is therefore too large. This is the standard NCERT result obtained from Ampere's law for an infinitely long conductor. A quick sanity check confirms the unit tesla and the order of magnitude $10^{-5}\text{T}$, which is typical for household currents at a few centimetres. Conceptually, the direction of this circulating field is fixed by the right-hand thumb rule: pointing the thumb along the conventional current makes the curled fingers trace the field loops, so the compass needle here would align tangent to a circle centred on the wire. This is why a current-carrying conductor placed near a magnetic compass deflects its needle, the very observation by Oersted that first revealed the deep link between electricity and magnetism and motivated the whole chapter.