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What is the magntiude of the integral of B over dl for part c? Enter in your answer in micro-T*m. Assume that all currents are 11.1 A.

What is the magntiude of the integral of B over dl for part c? Enter in your answer in micro-T*m. Assume that all currents are 11.1 A.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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What is the magntiude of the integral of B over dl for part c? Enter in your answer in micro-T*m. Assume that all currents are 11.1 A.

### Ampère's Law Evaluate \(\oint \vec{B} \cdot d\vec{l}\) for each of the cases shown in the accompanying figure. #### Diagrams Description - **Figure (a):** - An orange dashed loop encloses a wire carrying 2 A of current directed out of the loop. The magnetic field direction is indicated by the dashed loop arrows. - **Figure (b):** - An orange dashed loop encloses three wires carrying currents of 5 A, 2 A, and 6 A all directed into the loop. - **Figure (c):** - A small orange dashed loop is present, with a 3 A current flowing downward outside the loop and a 2 A current flowing upward and unclosed by the loop. - **Figure (d):** - An orange dashed loop encloses two wires, one carrying 2 A into the loop and another carrying 4 A out of it. Additional 3 A and 3 A currents are outside but not enclosed by the loop. - **Figure (e):** - An orange dashed loop encloses two wires; one carries 3 A into the loop, and another carries 2 A out of it. There are additional currents of 4 A and 2 A outside the loop, not affecting the enclosed calculation. ### Explanation Ampère's Law relates the integrated magnetic field around a closed loop to the electric current passing through the loop. For each case, calculate the total current enclosed by the loop. The net current through the loop affects the line integral \(\oint \vec{B} \cdot d\vec{l}\) by using the right-hand rule and considering the direction of current flow: - For **(a)**, only the 2 A current affects the loop. - For **(b)**, sum the currents enclosed by the loop: 5 A + 2 A + 6 A. - For **(c)**, the loop encloses no current. - For **(d)**, consider the algebraic sum of enclosed currents: 2 A in and 4 A out. - For **(e)**, calculate the algebraic sum of 3 A in and 2 A out.
Transcribed Image Text:### Ampère's Law Evaluate \(\oint \vec{B} \cdot d\vec{l}\) for each of the cases shown in the accompanying figure. #### Diagrams Description - **Figure (a):** - An orange dashed loop encloses a wire carrying 2 A of current directed out of the loop. The magnetic field direction is indicated by the dashed loop arrows. - **Figure (b):** - An orange dashed loop encloses three wires carrying currents of 5 A, 2 A, and 6 A all directed into the loop. - **Figure (c):** - A small orange dashed loop is present, with a 3 A current flowing downward outside the loop and a 2 A current flowing upward and unclosed by the loop. - **Figure (d):** - An orange dashed loop encloses two wires, one carrying 2 A into the loop and another carrying 4 A out of it. Additional 3 A and 3 A currents are outside but not enclosed by the loop. - **Figure (e):** - An orange dashed loop encloses two wires; one carries 3 A into the loop, and another carries 2 A out of it. There are additional currents of 4 A and 2 A outside the loop, not affecting the enclosed calculation. ### Explanation Ampère's Law relates the integrated magnetic field around a closed loop to the electric current passing through the loop. For each case, calculate the total current enclosed by the loop. The net current through the loop affects the line integral \(\oint \vec{B} \cdot d\vec{l}\) by using the right-hand rule and considering the direction of current flow: - For **(a)**, only the 2 A current affects the loop. - For **(b)**, sum the currents enclosed by the loop: 5 A + 2 A + 6 A. - For **(c)**, the loop encloses no current. - For **(d)**, consider the algebraic sum of enclosed currents: 2 A in and 4 A out. - For **(e)**, calculate the algebraic sum of 3 A in and 2 A out.
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