The magnitude J of the current density in a certain wire with a circular cross section of radius R = 2.00 mm is given by J = (3.34 x 108)r², with Jin amperes per square meter and radial distance r in meters. What is the current through the outer section bounded by r = 0.926R and r = R? Number i 2.392 Units mA
The magnitude J of the current density in a certain wire with a circular cross section of radius R = 2.00 mm is given by J = (3.34 x 108)r², with Jin amperes per square meter and radial distance r in meters. What is the current through the outer section bounded by r = 0.926R and r = R? Number i 2.392 Units mA
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![**Problem Statement:**
The magnitude \( J \) of the current density in a certain wire with a circular cross section of radius \( R = 2.00 \text{ mm} \) is given by:
\[ J = (3.34 \times 10^8) r^2 \]
where \( J \) is in amperes per square meter and \( r \) is the radial distance in meters. What is the current through the outer section bounded by \( r = 0.926R \) and \( r = R \)?
**Input Fields:**
- **Number:** 2.392
- **Units:** mA
To solve this problem, we need to integrate the current density \( J \) over the specified area to find the total current \( I \) passing through the outer section of the wire. The approach involves setting up and evaluating an integral with the given limits.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12c62ea9-2423-4a35-a6cd-74646c6bbd41%2F5bef7c0e-e141-40ab-9048-352e9248381c%2Fwsccq7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The magnitude \( J \) of the current density in a certain wire with a circular cross section of radius \( R = 2.00 \text{ mm} \) is given by:
\[ J = (3.34 \times 10^8) r^2 \]
where \( J \) is in amperes per square meter and \( r \) is the radial distance in meters. What is the current through the outer section bounded by \( r = 0.926R \) and \( r = R \)?
**Input Fields:**
- **Number:** 2.392
- **Units:** mA
To solve this problem, we need to integrate the current density \( J \) over the specified area to find the total current \( I \) passing through the outer section of the wire. The approach involves setting up and evaluating an integral with the given limits.
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