A closed curve encircles several conductors. The line integral ∮B ·d l⃗ around this curve is 3.8

Name: Problem 37, Chapter 28: University Physics with Modern Physics In SI Units
Uploaded: 2022-12-25T19:25:02-08:00
Duration: 2 min 33 s
Channel: Khaled Yasein
Description: A closed curve encircles several conductors. The line integral ∮B ·d l⃗ around this curve is 3.83 ×10^-4 T ·m. (a) What is the net cur- rent in the conductors? (b) If you were to integrate around the curve in the opposite direction, what would be the value of the line integral? Explain.

step 1 problem we have the closed loop line integral of the magnetic field around some curve that is su

Question

A closed curve encircles several conductors. The line integral $\oint \overrightarrow{\boldsymbol{B}} \cdot d \vec{l}$ around this curve is $3.83 \times 10^{-4} \mathrm{~T} \cdot \mathrm{m}$. (a) What is the net cur- rent in the conductors? (b) If you were to integrate around the curve in the opposite direction, what would be the value of the line integral? Explain.

    A closed curve encircles several conductors. The line integral $\oint \overrightarrow{\boldsymbol{B}} \cdot d \vec{l}$ around this curve is $3.83 \times 10^{-4} \mathrm{~T} \cdot \mathrm{m}$. (a) What is the net cur-
rent in the conductors? (b) If you were to integrate around the curve in the opposite direction, what would be the value of the line integral? Explain.

University Physics with Modern Physics In SI Units

Hugh D Young; Roger… 15th Edition

Chapter 28, Problem 37

Instant Answer

Solved by Expert Khaled Yasein

12/25/2022

Step 1

83 \times 10^{-4} \mathrm{~T} \cdot \mathrm{m}$. According to Ampere's law, this is equal to the magnetic permeability of free space $\mu_0$ multiplied by the enclosed current $I_{\text{enclosed}}$. Mathematically, this can be written as: \[\oint Show more…

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A closed curve encircles several conductors. The line integral $\oint \overrightarrow{\boldsymbol{B}} \cdot d \vec{l}$ around this curve is $3.83 \times 10^{-4} \mathrm{~T} \cdot \mathrm{m}$. (a) What is the net cur- rent in the conductors? (b) If you were to integrate around the curve in the opposite direction, what would be the value of the line integral? Explain.

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Key Concepts

Line Integral Orientation

The orientation of the integration path in a line integral is crucial, as reversing the path reverses the sign of the integral. This is due to the fact that the line integral depends on the direction in which the path is traversed. In the context of Ampere's Law, using the right-hand rule helps determine the sign of the net current enclosed by the path.

Ampere's Law

Ampere's Law relates the line integral of the magnetic field around a closed loop to the net current passing through the surface enclosed by that loop. It is mathematically expressed as ?B · dl = ??I_enc, where I_enc is the net current and ?? is the permeability of free space. This concept is central to understanding how magnetic fields are generated by electric currents.

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