The figure shows a cross section across a long cylindrical conductor of radius a = 1.88 cm carrying uniform current 71.4 A. What is the magnitude of the current's magnetic field at radial distance (a) 0, (b) 1.29 cm, (c) 1.88 cm (wire's surface), (d)3.01 cm? a (a) Number Units (b) Number Units (c) Number Units (d) Number Units

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Chapter1: Units, Trigonometry. And Vectors
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**Educational Content: Magnetic Field in Long Cylindrical Conductors**

The figure illustrates a cross section of a long cylindrical conductor with a radius \( a = 1.88 \, \text{cm} \) which carries a uniform current of \( 71.4 \, \text{A} \). The task is to determine the magnitude of the magnetic field at various radial distances from the center of the conductor. The specific distances are:

- (a) At \( 0 \, \text{cm} \) 
- (b) At \( 1.29 \, \text{cm} \)
- (c) At \( 1.88 \, \text{cm} \) (which corresponds to the surface of the wire)
- (d) At \( 3.01 \, \text{cm} \)

**Diagram Explanation:**
The diagram shows a circular cross-section of the cylindrical conductor. Within the circle, the following elements are marked:

- The radius \( a \) of the conductor.
- A radial distance \( r \) from the center, marking a specific point within or outside the conductor where the magnetic field might be measured.

**Questions:**

(a) **Enter the magnitude of the magnetic field at 0 cm:**
- Number: [Input required]
- Units: [Select from options]

(b) **Enter the magnitude of the magnetic field at 1.29 cm:**
- Number: [Input required]
- Units: [Select from options]

(c) **Enter the magnitude of the magnetic field at 1.88 cm (wire's surface):**
- Number: [Input required]
- Units: [Select from options]

(d) **Enter the magnitude of the magnetic field at 3.01 cm:**
- Number: [Input required]
- Units: [Select from options]

This exercise involves applying concepts related to magnetic fields in conductors, following principles such as Ampère’s Law, which states how current-producing electric fields create corresponding magnetic fields in their surroundings.
Transcribed Image Text:**Educational Content: Magnetic Field in Long Cylindrical Conductors** The figure illustrates a cross section of a long cylindrical conductor with a radius \( a = 1.88 \, \text{cm} \) which carries a uniform current of \( 71.4 \, \text{A} \). The task is to determine the magnitude of the magnetic field at various radial distances from the center of the conductor. The specific distances are: - (a) At \( 0 \, \text{cm} \) - (b) At \( 1.29 \, \text{cm} \) - (c) At \( 1.88 \, \text{cm} \) (which corresponds to the surface of the wire) - (d) At \( 3.01 \, \text{cm} \) **Diagram Explanation:** The diagram shows a circular cross-section of the cylindrical conductor. Within the circle, the following elements are marked: - The radius \( a \) of the conductor. - A radial distance \( r \) from the center, marking a specific point within or outside the conductor where the magnetic field might be measured. **Questions:** (a) **Enter the magnitude of the magnetic field at 0 cm:** - Number: [Input required] - Units: [Select from options] (b) **Enter the magnitude of the magnetic field at 1.29 cm:** - Number: [Input required] - Units: [Select from options] (c) **Enter the magnitude of the magnetic field at 1.88 cm (wire's surface):** - Number: [Input required] - Units: [Select from options] (d) **Enter the magnitude of the magnetic field at 3.01 cm:** - Number: [Input required] - Units: [Select from options] This exercise involves applying concepts related to magnetic fields in conductors, following principles such as Ampère’s Law, which states how current-producing electric fields create corresponding magnetic fields in their surroundings.
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