To determine the order of devices from greatest to weakest magnetic field strength, we need to calculate the magnetic field strength for each device. The formula to use is:
[tex]\[ B = \text{loops} \times \text{current} \times \text{core multiplier} \][/tex]
Where the core multiplier is 1 if the device has a metal core, and 0 if it doesn't. Let’s calculate the magnetic field strength for each device:
1. Device W:
- Loops: 60
- Current: 0.0 mA (0.0 A)
- Metal Core: yes (core multiplier = 1)
[tex]\[
B_W = 60 \times 0.0 \times 1 = 0.0
\][/tex]
2. Device X:
- Loops: 40
- Current: 0.2 mA (0.2 A)
- Metal Core: yes (core multiplier = 1)
[tex]\[
B_X = 40 \times 0.2 \times 1 = 8.0
\][/tex]
3. Device Y:
- Loops: 30
- Current: 0.1 mA (0.1 A)
- Metal Core: no (core multiplier = 0)
[tex]\[
B_Y = 30 \times 0.1 \times 0 = 0.0
\][/tex]
4. Device Z:
- Loops: 20
- Current: 0.1 mA (0.1 A)
- Metal Core: no (core multiplier = 0)
[tex]\[
B_Z = 20 \times 0.1 \times 0 = 0.0
\][/tex]
The magnetic field strengths are:
- [tex]\( B_W = 0.0 \)[/tex]
- [tex]\( B_X = 8.0 \)[/tex]
- [tex]\( B_Y = 0.0 \)[/tex]
- [tex]\( B_Z = 0.0 \)[/tex]
Now, ordering the devices from the greatest to the weakest magnetic field strength, we get:
1. Device X with [tex]\( B_X = 8.0 \)[/tex]
2. Device W with [tex]\( B_W = 0.0 \)[/tex]
3. Device Y with [tex]\( B_Y = 0.0 \)[/tex]
4. Device Z with [tex]\( B_Z = 0.0 \)[/tex]
So, the correct order from greatest to weakest is:
[tex]\[ X, W, Y, Z \][/tex]
Therefore, the correct answer is:
[tex]\[ X, W, Y, Z \][/tex]
