The figure shows a wire segment of length As = 3.5 cm, centered at the origin, carrying current i= 5.0 A in the positive y direction (as part of some complete circuit). To calculate the magnitude of the magnetic field B produced by the segment at a point several meters from the origin, we can use the Biot-Savart law as B = (H/4n)i As (sin 0)/r2. This is because r and 0 are essentially constant over the segment. Calculate B (in unit-vector notation) at the (x, y, z) coordinates (a) (0, 0, 6.2 m), (b) (0, 7.9 m, 0), (c) (9.6 m, 8.6 m, 0), and (d) (-5.1 m,-5.6 m,0). (a) (0,0, 6.2 m) = (Number i Units (b) |B| (0,7.9 m, 0) = Number i Units Units (c) B (9.6 m, 8.6 m, 0) = (Number i
The figure shows a wire segment of length As = 3.5 cm, centered at the origin, carrying current i= 5.0 A in the positive y direction (as part of some complete circuit). To calculate the magnitude of the magnetic field B produced by the segment at a point several meters from the origin, we can use the Biot-Savart law as B = (H/4n)i As (sin 0)/r2. This is because r and 0 are essentially constant over the segment. Calculate B (in unit-vector notation) at the (x, y, z) coordinates (a) (0, 0, 6.2 m), (b) (0, 7.9 m, 0), (c) (9.6 m, 8.6 m, 0), and (d) (-5.1 m,-5.6 m,0). (a) (0,0, 6.2 m) = (Number i Units (b) |B| (0,7.9 m, 0) = Number i Units Units (c) B (9.6 m, 8.6 m, 0) = (Number i
College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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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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![### Understanding Magnetic Field Calculation Using Biot-Savart Law
In this educational content, we delve into the calculation of the magnetic field \(\vec{B}\) produced by a current-carrying wire segment using the Biot-Savart law.
#### Problem Description
The figure illustrates a wire segment of length \(\Delta s = 3.5 \text{ cm}\), centered at the origin and carrying a current \(i = 5.0 \text{ A}\) in the positive y direction, which is a part of some complete circuit. To determine the magnitude of the magnetic field \(\vec{B}\) produced by this segment at a point that is several meters away from the origin, we will use the Biot-Savart law. The law is represented by:
\[
B = \left( \frac{\mu_0}{4\pi} \right) \frac{i \Delta s (\sin \theta)}{r^2}
\]
The parameters \(r\) and \(\theta\) remain essentially constant over the segment, and therefore can be used to determine \(\vec{B}\) at different coordinates. Below, \(\vec{B}\) is calculated in unit-vector notation at various coordinates specified as (x, y, z).
#### Coordinates and Calculations
The points of interest for calculating \(\vec{B}\) are:
- (a) \( (0, 0, 6.2 \text{ m}) \)
- (b) \( (0, 7.9 \text{ m}, 0) \)
- (c) \( (9.6 \text{ m}, 8.6 \text{ m}, 0) \)
- (d) \( (-5.1 \text{ m}, -5.6 \text{ m}, 0) \)
These points will be used to find the magnetic field in unit-vector notation.
#### Diagram Explanation
- The diagram shows a wire segment aligned along the y-axis with the current flowing upwards.
- \(\Delta s\) represents the length of the segment.
- Coordinate axes (x, y, z) are illustrated to orient the wire segment in a 3D space.
- Points are distributed strategically around the wire segment for \(\vec{B}\) calculation.
#### Calculation Interface
A user interface is provided to input values at different coordinates and units. Below](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8b65224-21df-49da-a8da-84f6a1af571d%2F61418099-1e7e-475f-8e2b-9e122442595e%2Faab5273_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Magnetic Field Calculation Using Biot-Savart Law
In this educational content, we delve into the calculation of the magnetic field \(\vec{B}\) produced by a current-carrying wire segment using the Biot-Savart law.
#### Problem Description
The figure illustrates a wire segment of length \(\Delta s = 3.5 \text{ cm}\), centered at the origin and carrying a current \(i = 5.0 \text{ A}\) in the positive y direction, which is a part of some complete circuit. To determine the magnitude of the magnetic field \(\vec{B}\) produced by this segment at a point that is several meters away from the origin, we will use the Biot-Savart law. The law is represented by:
\[
B = \left( \frac{\mu_0}{4\pi} \right) \frac{i \Delta s (\sin \theta)}{r^2}
\]
The parameters \(r\) and \(\theta\) remain essentially constant over the segment, and therefore can be used to determine \(\vec{B}\) at different coordinates. Below, \(\vec{B}\) is calculated in unit-vector notation at various coordinates specified as (x, y, z).
#### Coordinates and Calculations
The points of interest for calculating \(\vec{B}\) are:
- (a) \( (0, 0, 6.2 \text{ m}) \)
- (b) \( (0, 7.9 \text{ m}, 0) \)
- (c) \( (9.6 \text{ m}, 8.6 \text{ m}, 0) \)
- (d) \( (-5.1 \text{ m}, -5.6 \text{ m}, 0) \)
These points will be used to find the magnetic field in unit-vector notation.
#### Diagram Explanation
- The diagram shows a wire segment aligned along the y-axis with the current flowing upwards.
- \(\Delta s\) represents the length of the segment.
- Coordinate axes (x, y, z) are illustrated to orient the wire segment in a 3D space.
- Points are distributed strategically around the wire segment for \(\vec{B}\) calculation.
#### Calculation Interface
A user interface is provided to input values at different coordinates and units. Below
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