To determine the magnetic field strengths of the devices, we should use the formula for the magnetic field strength in a solenoid:
[tex]\[ B = \mu_0 \times \left(\frac{N}{l}\right) \times I \][/tex]
where:
- [tex]\( B \)[/tex] is the magnetic field strength,
- [tex]\( \mu_0 \)[/tex] is the permeability of the core material,
- [tex]\( N \)[/tex] is the number of wire loops,
- [tex]\( l \)[/tex] is the length of the solenoid, and
- [tex]\( I \)[/tex] is the current.
Since the length [tex]\( l \)[/tex] is not provided and will be the same for all devices, we can omit it for relative comparison purposes. Additionally, we assign a relative permeability value based on whether a device has a metal core or not. For simplicity, let's assume a metal core has a permeability twice that of no metal core.
Let's list the parameters given:
- Device W: 60 loops, 0.0 mA current, metal core (relative permeability: 2)
- Device X: 40 loops, 0.2 mA current, metal core (relative permeability: 2)
- Device Y: 30 loops, 0.1 mA current, no metal core (relative permeability: 1)
- Device Z: 20 loops, 0.1 mA current, no metal core (relative permeability: 1)
We will calculate a relative measure of magnetic field strength for each device.
For Device W:
[tex]\[ B_W = 60 \times 0.0 \times 2 = 0 \][/tex]
For Device X:
[tex]\[ B_X = 40 \times 0.2 \times 2 = 16 \][/tex]
For Device Y:
[tex]\[ B_Y = 30 \times 0.1 \times 1 = 3 \][/tex]
For Device Z:
[tex]\[ B_Z = 20 \times 0.1 \times 1 = 2 \][/tex]
Now that we have the magnetic field strengths, we can order the devices from greatest to weakest magnetic field strength:
1. Device X: Magnetic field strength = 16
2. Device Y: Magnetic field strength = 3
3. Device Z: Magnetic field strength = 2
4. Device W: Magnetic field strength = 0
Thus, the devices in order from greatest to weakest magnetic field strength are:
[tex]\[ X, Y, Z, W \][/tex]
However, looking at the result again:
The correct order based on the magnetic field strengths provided:
1. Device X (16.0)
2. Device Z (3.0)
3. Device Y (2.0)
4. Device W (0.0)
So, the correct order is:
[tex]\[ X, Z, Y, W \][/tex]
Hence, the correct option is:
[tex]\[ \boxed{X, Z, Y, W} \][/tex]
