**Title: Calculating Magnetic Fields Using Biot-Savart Law**---**Objective:**To use the Biot-Savart Law and Ampere’s Law to calculate magnetic fields and to explain the effects of changing magnetic fields using Faraday's Law of Induction.---**Problem Description:**A triangular framework is set up with a CO₂ ice block sliding on a pair of smooth rails. These rails are positioned 20 cm apart on an incline angled at 20°. A uniform magnetic field (\( B \)) is applied vertically downwards with a magnitude of 0.1 T. The task is to determine the constant speed at which the ice block slides down the rails.**Diagram Explanation:**The diagram shows a pair of parallel rails (represented by two lines) set at an incline. A block sits on the rails with arrows indicating the direction of motion and forces affecting it. The magnetic field is represented by arrows pointing downwards, indicating its vertical direction.**Solution Steps:**1. **Calculation of Gravitational Force Component:** - Calculate the gravitational force component along the incline using the weight of the CO₂ block and the inclination angle.2. **Magnetic Force Calculation Using Biot-Savart Law:** - Apply the Biot-Savart Law to determine the magnetic forces that act on the moving block along the rails.3. **Counteracting Forces Using Ampere’s Law:** - Consider forces acting perpendicularly provided by the current induced due to motion in the magnetic field, applying Ampere’s Law for detailed force interaction analysis.4. **Calculate Velocity using Faraday’s Law of Induction:** - Use Faraday’s Law to determine how the change in magnetic flux due to the motion of the block influences the system, enabling the calculation of velocity.5. **Concluding Calculation:** - Formulate an equation balancing forces and solve for the constant velocity of the sliding block.---**Conclusion:**This exercise demonstrates the integration of fundamental electromagnetic laws—Faraday’s, Biot-Savart, and Ampere’s— to solve practical physics problems involving magnetic fields and motion on inclined planes.

Answered: Image /qna-images/answer/3b2399a4-e879-4844-bfb7-741d3cf0622d.jpg

But-Savart Taw and Ampere's law, Apply fearaduy'y law of wry 6A G00a bar shder on Fails separateal by a distance' 200 cm ando located angle ahove The horizontale The rentorshoun is 3 Ro Auniferm masnetie field Co.GT) 1i dreeted vertically dowhwardcuer the entire region through which The har moves, What Conrtant speeed does the bur shder duwn The rails ? a pair of smouth an mcline plane that maner a 22° on

But-Savart Taw and Ampere's law, Apply fearaduy'y law of wry 6A G00a bar shder on Fails separateal by a distance' 200 cm ando located angle ahove The horizontale The rentorshoun is 3 Ro Auniferm masnetie field Co.GT) 1i dreeted vertically dowhwardcuer the entire region through which The har moves, What Conrtant speeed does the bur shder duwn The rails ? a pair of smouth an mcline plane that maner a 22° on

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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Concept explainers

Magnetic Field Of Coaxial Cable

The word coaxial means same axis. So for a long straight cable to be coaxial, it must have concentric cylindrical shaped conductor around it. Coaxial cable (popularly called ‘coax’) has various applications ranging from current conductors to radiofrequency signal transmitters. This cable has lower emission losses and provides protection from electromagnetic interference which allows signals with less power to transmit over longer distances.For example, currents produced in the pickup of a stereo turntable generally travel to the amplifier through a coaxial cable.The self-inductance of a coaxial cable is another important characteristic, because it influences the propagation of electrical signals in the cable.

Question

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**Title: Calculating Magnetic Fields Using Biot-Savart Law**

---

**Objective:**

To use the Biot-Savart Law and Ampere’s Law to calculate magnetic fields and to explain the effects of changing magnetic fields using Faraday's Law of Induction.

---

**Problem Description:**

A triangular framework is set up with a CO₂ ice block sliding on a pair of smooth rails. These rails are positioned 20 cm apart on an incline angled at 20°. A uniform magnetic field (\( B \)) is applied vertically downwards with a magnitude of 0.1 T. The task is to determine the constant speed at which the ice block slides down the rails.

**Diagram Explanation:**

The diagram shows a pair of parallel rails (represented by two lines) set at an incline. A block sits on the rails with arrows indicating the direction of motion and forces affecting it. The magnetic field is represented by arrows pointing downwards, indicating its vertical direction.

**Solution Steps:**

1. **Calculation of Gravitational Force Component:**
- Calculate the gravitational force component along the incline using the weight of the CO₂ block and the inclination angle.

2. **Magnetic Force Calculation Using Biot-Savart Law:**
- Apply the Biot-Savart Law to determine the magnetic forces that act on the moving block along the rails.

3. **Counteracting Forces Using Ampere’s Law:**
- Consider forces acting perpendicularly provided by the current induced due to motion in the magnetic field, applying Ampere’s Law for detailed force interaction analysis.

4. **Calculate Velocity using Faraday’s Law of Induction:**
- Use Faraday’s Law to determine how the change in magnetic flux due to the motion of the block influences the system, enabling the calculation of velocity.

5. **Concluding Calculation:**
- Formulate an equation balancing forces and solve for the constant velocity of the sliding block.

---

**Conclusion:**

This exercise demonstrates the integration of fundamental electromagnetic laws—Faraday’s, Biot-Savart, and Ampere’s— to solve practical physics problems involving magnetic fields and motion on inclined planes.

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