Physics - Magnetism Question with Solution | TestHub

The given conductor can be considered as a combination of an infinitely long straight wire and a circular loop of radius $r$.

1. Magnetic field due to the infinitely long straight wire at the center 'o':
The straight wire is at a perpendicular distance $r$ from the center 'o'.
Magnitude: $B_{straight}=\frac{{\mu }_{0}I}{2\pi r}$
Direction: According to the right-hand thumb rule, since the current is flowing towards the right and point 'o' is above the wire, the magnetic field at 'o' is directed outwards (perpendicular to the plane of the paper, $\odot$).

2. Magnetic field due to the circular loop at its center 'o':
Magnitude: $B_{loop}=\frac{{\mu }_{0}I}{2r}$
Direction: The current in the circular loop is flowing in a clockwise direction. According to the right-hand thumb rule, the magnetic field at the center 'o' is directed inwards (perpendicular to the plane of the paper, $\otimes$).

3. Net magnetic field at the center 'o':
Since the magnetic fields due to the straight wire and the circular loop are in opposite directions, the net magnetic induction is the difference of their magnitudes.
$B_{net}=B_{loop}-B_{straight}$
$B_{net}=\frac{{\mu }_{0}I}{2r}-\frac{{\mu }_{0}I}{2\pi r}$
$B_{net}=\frac{{\mu }_{0}I}{2\pi r}(\pi -1)$

Answer: $\frac{{\mu }_0\mathrm{I}}{2\pi \mathrm{r}}(\pi -1)$