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Straight Wire Segment A straight wire segment of length I makes an angle of 23 degrees with respect to the axis. The wire carries a current of 8.7 A in the direction shown in the figure. There is a magnetic field in the vicinity of the wire which points in the negative z direction with a magnitude given by B = Bo(+)³, where Bo = 5.4 T and L = 2.18 m. Force X Torque X X X X X X X L X X X X X X X X X X X X X ➜ B(x) What is the component of the force on the wire segment? force= If the wire is free to rotate about the z axis, what is the magnitude of the torque on the wire segment? torque=

Straight Wire Segment A straight wire segment of length I makes an angle of 23 degrees with respect to the axis. The wire carries a current of 8.7 A in the direction shown in the figure. There is a magnetic field in the vicinity of the wire which points in the negative z direction with a magnitude given by B = Bo(+)³, where Bo = 5.4 T and L = 2.18 m. Force X Torque X X X X X X X L X X X X X X X X X X X X X ➜ B(x) What is the component of the force on the wire segment? force= If the wire is free to rotate about the z axis, what is the magnitude of the torque on the wire segment? torque=

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I have been trying this problem for a while and I am stuck. I tried doing some integrals after doing the cross product, but nothing seems to be working.

## Straight Wire Segment A straight wire segment of length \( L \) makes an angle of 23 degrees with respect to the \( x \) axis. The wire carries a current of 8.7 A in the direction shown in the figure. There is a magnetic field in the vicinity of the wire which points in the negative \( z \) direction with a magnitude given by \( B = B_0 \left( \frac{x}{L} \right)^3 \), where \( B_0 = 5.4 \, \text{T} \) and \( L = 2.18 \, \text{m} \). ### Diagram Explanation The diagram shows a straight wire labeled as \( L \), at an angle \( \theta \) with respect to the \( x \) axis. The current \( I \) flows along the wire. The magnetic field \( \mathbf{B}(x) \) is depicted as pointing into the page, represented by crosses (×), indicating its direction is along the negative \( z \)-axis. ### Force **Question:** What is the \( x \) component of the force on the wire segment? - **Force Component:** \[ \text{force} = \underline{\hspace{4cm}} \] ### Torque **Question:** If the wire is free to rotate about the \( z \) axis, what is the magnitude of the torque on the wire segment? - **Torque:** \[ \text{torque} = \underline{\hspace{4cm}} \]
Transcribed Image Text:## Straight Wire Segment A straight wire segment of length \( L \) makes an angle of 23 degrees with respect to the \( x \) axis. The wire carries a current of 8.7 A in the direction shown in the figure. There is a magnetic field in the vicinity of the wire which points in the negative \( z \) direction with a magnitude given by \( B = B_0 \left( \frac{x}{L} \right)^3 \), where \( B_0 = 5.4 \, \text{T} \) and \( L = 2.18 \, \text{m} \). ### Diagram Explanation The diagram shows a straight wire labeled as \( L \), at an angle \( \theta \) with respect to the \( x \) axis. The current \( I \) flows along the wire. The magnetic field \( \mathbf{B}(x) \) is depicted as pointing into the page, represented by crosses (×), indicating its direction is along the negative \( z \)-axis. ### Force **Question:** What is the \( x \) component of the force on the wire segment? - **Force Component:** \[ \text{force} = \underline{\hspace{4cm}} \] ### Torque **Question:** If the wire is free to rotate about the \( z \) axis, what is the magnitude of the torque on the wire segment? - **Torque:** \[ \text{torque} = \underline{\hspace{4cm}} \]
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