The figure shows a wire segment of length As = 4.2 cm, centered at the origin, carrying current i = 2.3 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 = (µ/41)iAs (sin 0)/r². This is because r and e are essentially constant over the segment. Calculate B (in unit-vector notation) at the (x, y, z) coordinates (a) (0, 0, 6.5 m), (b) (0, 8.7 m, 0), (c) (9.6 m, 9.6 m, 0), and (d) (-5.8 m,-6.5 m,0). As- (a) B (0,0, 6.5 m) = (Number i Units (b) |B| (0,8.7 m, 0) = Number i Units (c) B (9.6 m, 9.6 m, 0) = (Number i Units (d) B (-5.8 m,-6.5 m,0) = (Number i Units
The figure shows a wire segment of length As = 4.2 cm, centered at the origin, carrying current i = 2.3 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 = (µ/41)iAs (sin 0)/r². This is because r and e are essentially constant over the segment. Calculate B (in unit-vector notation) at the (x, y, z) coordinates (a) (0, 0, 6.5 m), (b) (0, 8.7 m, 0), (c) (9.6 m, 9.6 m, 0), and (d) (-5.8 m,-6.5 m,0). As- (a) B (0,0, 6.5 m) = (Number i Units (b) |B| (0,8.7 m, 0) = Number i Units (c) B (9.6 m, 9.6 m, 0) = (Number i Units (d) B (-5.8 m,-6.5 m,0) = (Number i Units
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![**Biot-Savart Law Application to a Wire Segment**
The figure illustrates a wire segment of length \( \Delta s = 4.2 \, \text{cm} \), centered at the origin. It carries a current \( i = 2.3 \, \text{A} \) in the positive \( y \)-direction, as part of a complete circuit. To find the magnetic field \( \vec{B} \) produced by the segment at a point several meters from the origin, we utilize the Biot-Savart law:
\[
B = \left( \frac{\mu_0}{4 \pi} \right) \frac{\Delta s (\sin \theta)}{r^2}
\]
where \( r \) and \( \theta \) remain constant over the segment. You need to calculate \( \vec{B} \) in unit-vector notation at the given coordinates:
1. **Coordinate (a) \((0, 0, 6.5 \, \text{m})\):**
\[
\vec{B} = ( \text{Number} \, \text{unit} ) \, \hat{\imath}
\]
2. **Coordinate (b) \((0, 8.7 \, \text{m}, 0)\):**
\[
|\vec{B}| = \text{Number} \, \text{unit}
\]
3. **Coordinate (c) \((9.6 \, \text{m}, 9.6 \, \text{m}, 0)\):**
\[
\vec{B} = ( \text{Number} \, \text{unit} ) \, \hat{\jmath}
\]
4. **Coordinate (d) \((-5.8 \, \text{m}, -6.5 \, \text{m}, 0)\):**
\[
\vec{B} = ( \text{Number} \, \text{unit} ) \, \hat{k}
\]
**Diagram Explanation:**
The diagram shows a cylindrical segment of wire aligned along the \( y \)-axis. The \( x, y, \) and \( z \) axes are marked, indicating the orientation of the wire in three-dimensional space. This helps visualize how the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4da129a-7b5e-40d2-96f8-baa05141b9b9%2Fb819f6a4-2780-4960-a933-c88b41862d8e%2F0ia44nj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Biot-Savart Law Application to a Wire Segment**
The figure illustrates a wire segment of length \( \Delta s = 4.2 \, \text{cm} \), centered at the origin. It carries a current \( i = 2.3 \, \text{A} \) in the positive \( y \)-direction, as part of a complete circuit. To find the magnetic field \( \vec{B} \) produced by the segment at a point several meters from the origin, we utilize the Biot-Savart law:
\[
B = \left( \frac{\mu_0}{4 \pi} \right) \frac{\Delta s (\sin \theta)}{r^2}
\]
where \( r \) and \( \theta \) remain constant over the segment. You need to calculate \( \vec{B} \) in unit-vector notation at the given coordinates:
1. **Coordinate (a) \((0, 0, 6.5 \, \text{m})\):**
\[
\vec{B} = ( \text{Number} \, \text{unit} ) \, \hat{\imath}
\]
2. **Coordinate (b) \((0, 8.7 \, \text{m}, 0)\):**
\[
|\vec{B}| = \text{Number} \, \text{unit}
\]
3. **Coordinate (c) \((9.6 \, \text{m}, 9.6 \, \text{m}, 0)\):**
\[
\vec{B} = ( \text{Number} \, \text{unit} ) \, \hat{\jmath}
\]
4. **Coordinate (d) \((-5.8 \, \text{m}, -6.5 \, \text{m}, 0)\):**
\[
\vec{B} = ( \text{Number} \, \text{unit} ) \, \hat{k}
\]
**Diagram Explanation:**
The diagram shows a cylindrical segment of wire aligned along the \( y \)-axis. The \( x, y, \) and \( z \) axes are marked, indicating the orientation of the wire in three-dimensional space. This helps visualize how the
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