Does the absolute value of the line integral of the magnetic field of the flat segment increase, decrease, or remain the same when the second wire is added and why

College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Does the absolute value of the line integral of the magnetic field of the flat segment increase, decrease, or remain the same when the second wire is added and why

### Explanation of Ampere's Law with Diagram

Consider an Amperian loop consisting of one curved segment and a flat segment around a wire with current directed out of the page. Another wire with current directed into the page is added as shown.

**Diagrams:**

- **Before Adding the Second Wire:**
  - The loop is depicted with a dashed line forming an oval shape with a flat segment on the right.
  - The wire carries a current \( I \) directed out of the page, represented by the symbol ⊙ (dot within a circle).
  - The segment labeled "curve" forms the left portion of the loop.

- **After Adding the Second Wire:**
  - The loop remains similar with a flat segment on the right labeled "flat".
  - The first wire still carries a current \( I \) directed out of the page (⊙).
  - An additional wire is shown with current \( I \) directed into the page, represented by the symbol ⊗ (cross within a circle).

These diagrams illustrate the concept of using Amperian loops to apply Ampere's Law in magnetic field calculations around current-carrying wires.
Transcribed Image Text:### Explanation of Ampere's Law with Diagram Consider an Amperian loop consisting of one curved segment and a flat segment around a wire with current directed out of the page. Another wire with current directed into the page is added as shown. **Diagrams:** - **Before Adding the Second Wire:** - The loop is depicted with a dashed line forming an oval shape with a flat segment on the right. - The wire carries a current \( I \) directed out of the page, represented by the symbol ⊙ (dot within a circle). - The segment labeled "curve" forms the left portion of the loop. - **After Adding the Second Wire:** - The loop remains similar with a flat segment on the right labeled "flat". - The first wire still carries a current \( I \) directed out of the page (⊙). - An additional wire is shown with current \( I \) directed into the page, represented by the symbol ⊗ (cross within a circle). These diagrams illustrate the concept of using Amperian loops to apply Ampere's Law in magnetic field calculations around current-carrying wires.
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