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?

Question

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.

Sebastian Acosta · Accepted Answer

#(x,y)=(0.115, 0.164)#

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^@#. 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=muH# Or #B=(mu mu_@I)/(2pir)# Inserting given values we get #0.2423xx10^-3=(250xx4pixx10^-7xx969xx10^-3)/(2pir)# #=>r=(250xx4pixx10^-7xx969xx10^-3)/(2pixx0.2423xx10^-3)# #r=0.2m# Finding out #x and y# coordinates #x=0.2cos55^@=0.115m#, rounded to three decimal places #y=0.2sin55^@=0.164m#, rounded to three decimal places

Emily Abbate · Answer

undefined To find the x and y coordinates of the location, we can use trigonometry. Given that the magnetic field is directed at an angle of 55°, we can use the cosine and sine functions to determine the x and y components of the field. The x component (Bx) can be calculated as B * cos(θ), and the y component (By) can be calculated as B * sin(θ), where B is the magnitude of the magnetic field (0.2423 mT) and θ is the angle (55°).

Using these formulas:
Bx = 0.2423 mT * cos(55°) ≈ 0.2423 mT * 0.5736 ≈ 0.1389 mT
By = 0.2423 mT * sin(55°) ≈ 0.2423 mT * 0.8192 ≈ 0.1985 mT

So the x coordinate is approximately 0.1389 meters and the y coordinate is approximately 0.1985 meters.