# If the magnetic field is measured to have a strength of 242.25μT directed at an angle of 325°, what is the location of this measurement?

## A wire carrying 969mA is travelling upwards along the Z axis through four different materials, one in each quadrant. The first quadrant is composed of cobalt; the second quadrant has iron, the third quadrant is made of nickel, and the 4th quadrant is air.

As the measurement of magnetic field were taken along an angle of ${325}^{\circ}$, the point of observation lies in the fourth quadrant.
It is given that this quadrant is composed of air. We know that the strength of the magnetic field $\vec{B}$ depends on the current $I$ in the wire and the distance $r$ from the wire. The expression is
$| \vec{B} | = \frac{{\mu}_{\circ} I}{2 \pi r}$
where ${\mu}_{\circ}$ is the magnetic permeability of free space and is $4 \pi \times {10}^{-} 7 T m {A}^{-} 1$.
$242.25 \times {10}^{-} 6 = \frac{4 \pi \times {10}^{-} 7 \times 969 \times {10}^{-} 3}{2 \pi r}$
$\implies r = \frac{4 \pi \times {10}^{-} 7 \times 969 \times {10}^{-} 3}{2 \pi \times 242.25 \times {10}^{-} 6}$
$\implies r = 8 \times {10}^{-} 4 m$