### Magnetic Line Integral Problem**Problem:**What is the line integral of \(\vec{B}\) between points "i" and "f" in the figure below?**Answer Choices:**A) \(0.00 \ [\text{Tm}]\) B) \(1.26 \times 10^{-6} \ [\text{Tm}]\) C) \(2.51 \times 10^{-6} \ [\text{Tm}]\) D) \(4.00 \times 10^{-5} \ [\text{Tm}]\) E) None of the above **Diagram Description:**- **Integration Path:** The integration path is depicted as a semicircular arc with radius 1.0 cm, curved around a vertical wire carrying a current of 2.0 A.- **Points i and f:** These are the start and end points of the integration path, lying on the straight horizontal lines extending to the left and right of the semicircle respectively.- **Distance:** The total straight-line distance between points i and f is 6.0 cm.- **Current:** The wire positioned perpendicularly through the center of the semicircle carries a current of 2.0 A upward (indicated by the dot with a circle). By using Ampère's law and calculating the line integral of the magnetic field \(\vec{B}\) around the path, we can determine the correct answer from the given choices.

Answered: Image /qna-images/answer/ae8b6475-d888-4bae-82d2-c89e1483b782.jpg

What is the line integral of B between points “i" and “f" in the figure below? A) 0.00 [Tm] 1.0 cm B) 1.26 × 10-6 [Tm] -Integration path C) 2.51 × 10-6 [Tm] D) 4.00 × 10-5 [Tm] E) None of above 2.0 A 6.0 cm

What is the line integral of B between points “i" and “f" in the figure below? A) 0.00 [Tm] 1.0 cm B) 1.26 × 10-6 [Tm] -Integration path C) 2.51 × 10-6 [Tm] D) 4.00 × 10-5 [Tm] E) None of above 2.0 A 6.0 cm

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.

Question

### Magnetic Line Integral Problem

**Problem:**
What is the line integral of \(\vec{B}\) between points "i" and "f" in the figure below?

**Answer Choices:**
A) \(0.00 \ [\text{Tm}]\)
B) \(1.26 \times 10^{-6} \ [\text{Tm}]\)
C) \(2.51 \times 10^{-6} \ [\text{Tm}]\)
D) \(4.00 \times 10^{-5} \ [\text{Tm}]\)
E) None of the above

**Diagram Description:**

- **Integration Path:** The integration path is depicted as a semicircular arc with radius 1.0 cm, curved around a vertical wire carrying a current of 2.0 A.
- **Points i and f:** These are the start and end points of the integration path, lying on the straight horizontal lines extending to the left and right of the semicircle respectively.
- **Distance:** The total straight-line distance between points i and f is 6.0 cm.
- **Current:** The wire positioned perpendicularly through the center of the semicircle carries a current of 2.0 A upward (indicated by the dot with a circle).

By using Ampère's law and calculating the line integral of the magnetic field \(\vec{B}\) around the path, we can determine the correct answer from the given choices.

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