# At another location, the magnetic field is found to be 0.2423mT directed 55°. What are the x and y coordinates of this location, measured in meters?

## 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.

Aug 31, 2016

$\left(x , y\right) = \left(0.115 , 0.164\right)$

#### Explanation:

Another location is with respect to first location described in first part of this question here.

Taking it further. now the point of observation is ${55}^{\circ}$. Implies that it is located in first quadrant. It is given that first quadrant is composed of cobalt. Maximum Relative permeability of 99% pure cobalt is 250.
As such we know that for ferromagnetic substances
$B = \mu H$
Or $B = \frac{\mu {\mu}_{\circ} I}{2 \pi r}$
Inserting given values we get
$0.2423 \times {10}^{-} 3 = \frac{250 \times 4 \pi \times {10}^{-} 7 \times 969 \times {10}^{-} 3}{2 \pi r}$
$\implies r = \frac{250 \times 4 \pi \times {10}^{-} 7 \times 969 \times {10}^{-} 3}{2 \pi \times 0.2423 \times {10}^{-} 3}$
$r = 0.2 m$
Finding out $x \mathmr{and} y$ coordinates
$x = 0.2 \cos {55}^{\circ} = 0.115 m$, rounded to three decimal places
$y = 0.2 \sin {55}^{\circ} = 0.164 m$, rounded to three decimal places