Please type the final answer instead of hand writting **Educational Content: Magnetic Potential Energy and Magnetic Torque of a Coil**---**Problem Statement:**The coil in the figure carries current \( i = 1.83 \text{ A} \) in the direction indicated, is parallel to an xz-plane, has 4 turns and an area of \( 5.89 \times 10^{-3} \text{ m}^2 \), and lies in a uniform magnetic field \(\vec{B} = (1.73 \hat{i} - 2.49 \hat{j} - 3.73 \hat{k}) \text{ mT} \).**Questions:**(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?---**Solution:**(a) **Magnetic Potential Energy Calculation:**- **Number:** -1.07E-4 - **Unit:** \(\mu\text{J}\)(b) **Magnetic Torque Calculation:**- \(\hat{i}\) component: 3.89E-3- \(\hat{j}\) component: 0- \(\hat{k}\) component: 8.14E-5 - **Unit:** \(\mu\text{N} \cdot \text{m}\)---**Explanation of Diagram:**The image features a coil positioned parallel to an xz-plane with current \( i \) flowing in the direction indicated by an arrow. The magnetic field \(\vec{B}\) is denoted by the components \(1.73 \hat{i} - 2.49 \hat{j} - 3.73 \hat{k} \text{ mT} \). The arrows on the diagram represent both the direction of the current in the coil and the direction of the coordinate axes (x, y, z).- **Figure Key Elements:** - A circular coil laying in the xz-plane. - Coordinate system \((x, y, z)\) illustrated for spatial orientation. - Arrow indicating the direction of electric current \(i\).---This problem encompasses the principles of electromagnetism, involving concepts such as magnetic potential energy and magnetic torque in a uniform magnetic field.

Answered: Image /qna-images/answer/057b1b35-b8eb-4a07-a8bb-a0bc2ea8a7c4.jpg

Your answer is partially correct. The coil in the figure carries current i = 1.83A in the direction indicated, is parallel to an xz plane, has 4 turns and an area of 5.89 x 103 m2, and lies in a uniform magnetic field B = (1.737-2.49j-3.73 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 i -1.07E-4 Unit (b) Number ( i+0 k) Unit 3.89E-3 8.14E-5 UN'm

Your answer is partially correct. The coil in the figure carries current i = 1.83A in the direction indicated, is parallel to an xz plane, has 4 turns and an area of 5.89 x 103 m2, and lies in a uniform magnetic field B = (1.737-2.49j-3.73 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 i -1.07E-4 Unit (b) Number ( i+0 k) Unit 3.89E-3 8.14E-5 UN'm

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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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Question

Please type the final answer instead of hand writting

**Educational Content: Magnetic Potential Energy and Magnetic Torque of a Coil**

---

**Problem Statement:**

The coil in the figure carries current \( i = 1.83 \text{ A} \) in the direction indicated, is parallel to an xz-plane, has 4 turns and an area of \( 5.89 \times 10^{-3} \text{ m}^2 \), and lies in a uniform magnetic field \(\vec{B} = (1.73 \hat{i} - 2.49 \hat{j} - 3.73 \hat{k}) \text{ mT} \).

**Questions:**
(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?

---

**Solution:**

(a) **Magnetic Potential Energy Calculation:**

- **Number:** -1.07E-4
- **Unit:** \(\mu\text{J}\)

(b) **Magnetic Torque Calculation:**

- \(\hat{i}\) component: 3.89E-3
- \(\hat{j}\) component: 0
- \(\hat{k}\) component: 8.14E-5
- **Unit:** \(\mu\text{N} \cdot \text{m}\)

---

**Explanation of Diagram:**

The image features a coil positioned parallel to an xz-plane with current \( i \) flowing in the direction indicated by an arrow. The magnetic field \(\vec{B}\) is denoted by the components \(1.73 \hat{i} - 2.49 \hat{j} - 3.73 \hat{k} \text{ mT} \). The arrows on the diagram represent both the direction of the current in the coil and the direction of the coordinate axes (x, y, z).

- **Figure Key Elements:**
- A circular coil laying in the xz-plane.
- Coordinate system \((x, y, z)\) illustrated for spatial orientation.
- Arrow indicating the direction of electric current \(i\).

---

This problem encompasses the principles of electromagnetism, involving concepts such as magnetic potential energy and magnetic torque in a uniform magnetic field.

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