The coil in the figure carries current i = 1.70 A in the direction indicated, is parallel to an xz plane, has 6 turns and an area of 5.59 × 10-³ m², and lies in a uniform magnetic field B = (1.53 î - 3.56 - 3.67 k) mT. (a) What is the magnetic potential energy of the coil-magnetic field system? (b) What is the magnetic torque (in unit-vector notation) on the coil? (a) Number Unit J (b) Number ( i î+ IM Ĵ+ K) Unit uN*m y

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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Transcription for Educational Website:**

The coil in the figure carries a current \( i = 1.70 \, \text{A} \) in the direction indicated, is parallel to an \( xz \) plane, has 6 turns, and an area of \( 5.59 \times 10^{-3} \, \text{m}^2 \). It lies in a uniform magnetic field \( \mathbf{B} = (1.53 \, \hat{\mathbf{i}} - 3.56 \, \hat{\mathbf{j}} - 3.67 \, \hat{\mathbf{k}}) \, \text{mT} \).

**(a)** What is the magnetic potential energy of the coil-magnetic field system?

- [ ] Number: [Input Box]  
- Unit: \(\mu\text{J}\)

**(b)** What is the magnetic torque (in unit-vector notation) on the coil?

- [ ] Number: [Input Box]  
\(\hat{\mathbf{i}}\) + [Input Box]  
\(\hat{\mathbf{j}}\) + [Input Box]  
\(\hat{\mathbf{k}}\)

- Unit: \(\mu\text{N*m}\)

**Diagram Explanation:**

The diagram shows a coil oriented parallel to the \( xz \) plane, with a current labeled as \( i \) flowing in the indicated direction. The axes \( x \), \( y \), and \( z \) are clearly marked, demonstrating the spatial orientation of the coil with respect to the magnetic field vectors.
Transcribed Image Text:**Transcription for Educational Website:** The coil in the figure carries a current \( i = 1.70 \, \text{A} \) in the direction indicated, is parallel to an \( xz \) plane, has 6 turns, and an area of \( 5.59 \times 10^{-3} \, \text{m}^2 \). It lies in a uniform magnetic field \( \mathbf{B} = (1.53 \, \hat{\mathbf{i}} - 3.56 \, \hat{\mathbf{j}} - 3.67 \, \hat{\mathbf{k}}) \, \text{mT} \). **(a)** What is the magnetic potential energy of the coil-magnetic field system? - [ ] Number: [Input Box] - Unit: \(\mu\text{J}\) **(b)** What is the magnetic torque (in unit-vector notation) on the coil? - [ ] Number: [Input Box] \(\hat{\mathbf{i}}\) + [Input Box] \(\hat{\mathbf{j}}\) + [Input Box] \(\hat{\mathbf{k}}\) - Unit: \(\mu\text{N*m}\) **Diagram Explanation:** The diagram shows a coil oriented parallel to the \( xz \) plane, with a current labeled as \( i \) flowing in the indicated direction. The axes \( x \), \( y \), and \( z \) are clearly marked, demonstrating the spatial orientation of the coil with respect to the magnetic field vectors.
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