Certainly! Let's break down the problem step-by-step:
### Given:
1. Dimensions of the rectangular coil:
- Length ([tex]\(L\)[/tex]) = 5.04 meters.
- Width ([tex]\(W\)[/tex]) = 8.50 centimeters (convert to meters: [tex]\(W\)[/tex] = 8.50 cm × 0.01 = 0.085 meters).
2. Characteristics of the coil:
- Number of turns ([tex]\(N\)[/tex]) = 25.
- Current ([tex]\(I\)[/tex]) = 15.0 milliamperes (convert to amperes: [tex]\(I\)[/tex] = 15.0 mA × 0.001 = 0.015 amperes).
3. Magnetic field ([tex]\(B\)[/tex]):
- Magnetic field ([tex]\(B\)[/tex]) = 0.3507 Tesla.
### Calculate the Area of the Rectangular Coil:
- The area ([tex]\(A\)[/tex]) of the rectangle can be calculated using its length and width.
[tex]\[ A = L \times W \][/tex]
[tex]\[ A = 5.04 \, \text{meters} \times 0.085 \, \text{meters} \][/tex]
[tex]\[ A = 0.4284 \, \text{square meters} \][/tex]
### Calculate the Magnetic Moment:
- The magnetic moment ([tex]\(m\)[/tex]) can be calculated using the number of turns, current, and area.
[tex]\[ m = N \times I \times A \][/tex]
[tex]\[ m = 25 \times 0.015 \, \text{amperes} \times 0.4284 \, \text{square meters} \][/tex]
[tex]\[ m = 0.16065 \, \text{ampere-square meters} \][/tex]
### Calculate the Torque:
- The torque ([tex]\(\tau\)[/tex]) acting on the coil is calculated using the magnetic moment and the magnetic field.
[tex]\[ \tau = m \times B \][/tex]
[tex]\[ \tau = 0.16065 \, \text{ampere-square meters} \times 0.3507 \, \text{Tesla} \][/tex]
[tex]\[ \tau = 0.05634 \, \text{Newton meters} \][/tex]
### Summary
- Length of the coil: 5.04 meters.
- Width of the coil: 8.50 centimeters ([tex]\(0.085\)[/tex] meters).
- Number of turns: 25.
- Current: 15.0 milliamperes ([tex]\(0.015\)[/tex] amperes).
- Magnetic field: 0.3507 Tesla.
- Area of the coil: [tex]\(0.4284\)[/tex] square meters.
- Magnetic moment: [tex]\(0.16065\)[/tex] ampere-square meters.
- Torque: [tex]\(0.05634\)[/tex] Newton meters.
