Question: Calculate the direction of Earth's magnetic field.
3 components of the magnetic field:
Geographic South to North: 0.01670 mT
Geographic West to East: 0.002147 mT
Up to down (up is the sky, down is the ground): 0.03722 mT
Calculating angle East of North:
tanθ=0.002147/0.01670
θ=7.33° East of North
Angle below horizontal:
tanθ=0.03722/√(0.01670^2+0.002147^2)
θ=65.66° below horizontal
Is my attempt correct?
If I did the first question correctly, I need help with this question:
Compare the direction of the projection of this magnetic field vector on the horizontal
plane (the angle to the east (or west) of geographic north) with the direction of the
compass.
I honestly don't understand what they're asking here. Are they saying to compare 7.33° with the direction of the compass? How do I find the direction of the compass?
Also, one last question:
The magnetic field in anywhere between two helmholtz coils is uniform, right?
Your attempt to calculate the direction of Earth's magnetic field seems correct. Here's a breakdown of your calculations:
To calculate the angle east of north, you used the formula tan(θ) = (east component)/(north component). By dividing the east component of 0.002147 mT by the north component of 0.01670 mT, you obtained tan(θ) = 0.1286. Taking the inverse tangent of this value, you found θ ≈ 7.33° east of north.
To calculate the angle below the horizontal, you used the formula tan(θ) = (down component)/(magnitude of horizontal component). By dividing the down component of 0.03722 mT by the magnitude of the horizontal component (√((0.01670 mT)^2 + (0.002147 mT)^2)), you obtained tan(θ) ≈ 2.23. Taking the inverse tangent of this value, you found θ ≈ 65.66° below the horizontal.
Regarding your question about comparing the direction of the projection of the magnetic field vector on the horizontal plane with the direction of the compass, it seems that they want you to compare the angle of 7.33° east of north with the direction indicated by a compass. The direction of the compass refers to the orientation of the needle, which typically aligns with Earth's magnetic field.
To find the direction of the compass, you can simply observe the needle of a functional compass. The needle points towards the magnetic north pole. So, compare the angle you calculated (7.33° east of north) with the direction indicated by a compass needle.
Lastly, you asked whether the magnetic field is uniform between two Helmholtz coils. In general, the magnetic field between two Helmholtz coils is relatively uniform within the region between the coils. However, it is important to note that the uniformity of the magnetic field depends on various factors such as the design, dimensions, and placement of the coils. In practice, imperfections and external factors may cause deviations from perfect uniformity.