A wire carries an I₁ = 7.35-A current along the x-axis, and another wire carries an I₂ = 5.30-A current along the y-axis, as shown in the figure below. What is the magnetic field at point P, located at x = 4.00 m, y = 3.00 m? magnitude. direction ---Select--- UT
A wire carries an I₁ = 7.35-A current along the x-axis, and another wire carries an I₂ = 5.30-A current along the y-axis, as shown in the figure below. What is the magnetic field at point P, located at x = 4.00 m, y = 3.00 m? magnitude. direction ---Select--- UT
College Physics
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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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![**Problem Statement:**
A wire carries an \( I_1 = 7.35 \)-A current along the x-axis, and another wire carries an \( I_2 = 5.30 \)-A current along the y-axis, as shown in the figure below. What is the magnetic field at point \( P \), located at \( x = 4.00 \) m, \( y = 3.00 \) m?
**Figure Description:**
The diagram provided shows two perpendicular wires, one along the x-axis and the other along the y-axis. The wire along the x-axis carries a current \( I_1 \) of 7.35 A, moving to the right. The wire along the y-axis carries a current \( I_2 \) of 5.30 A, moving upward. Point \( P \) is located at the coordinates \( (4.00, 3.00) \) m relative to the origin where the wires intersect. The graph includes arrows indicating the directions of the currents along their respective axes.
Below the description, there is an input field for the magnitude of the magnetic field at point \( P \), in microteslas (µT), and a dropdown menu to select the direction.
**Interactive Inputs:**
- **Magnitude:** Textbox to enter the magnetic field's magnitude.
- **Direction:** Dropdown menu to select the direction.
**Analysis:**
To determine the magnetic field at point \( P \) due to the currents in the wires, we should apply the Biot-Savart law or Ampère’s law for long straight wires.
The magnitude of the magnetic field due to a long straight current-carrying wire at a distance \( r \) from the wire is given by:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
Where:
- \( B \) is the magnetic field.
- \( \mu_0 \) is the permeability of free space (\( 4\pi \times 10^{-7} \) T·m/A).
- \( I \) is the current.
- \( r \) is the distance from the wire to the point in question.
The directions of the magnetic fields created by each wire can be determined using the right-hand rule.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fe3cb2f-b243-4382-966f-eceede055ec9%2Fa6756465-13fe-4e01-a645-eef99b2920f2%2Flssg81_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A wire carries an \( I_1 = 7.35 \)-A current along the x-axis, and another wire carries an \( I_2 = 5.30 \)-A current along the y-axis, as shown in the figure below. What is the magnetic field at point \( P \), located at \( x = 4.00 \) m, \( y = 3.00 \) m?
**Figure Description:**
The diagram provided shows two perpendicular wires, one along the x-axis and the other along the y-axis. The wire along the x-axis carries a current \( I_1 \) of 7.35 A, moving to the right. The wire along the y-axis carries a current \( I_2 \) of 5.30 A, moving upward. Point \( P \) is located at the coordinates \( (4.00, 3.00) \) m relative to the origin where the wires intersect. The graph includes arrows indicating the directions of the currents along their respective axes.
Below the description, there is an input field for the magnitude of the magnetic field at point \( P \), in microteslas (µT), and a dropdown menu to select the direction.
**Interactive Inputs:**
- **Magnitude:** Textbox to enter the magnetic field's magnitude.
- **Direction:** Dropdown menu to select the direction.
**Analysis:**
To determine the magnetic field at point \( P \) due to the currents in the wires, we should apply the Biot-Savart law or Ampère’s law for long straight wires.
The magnitude of the magnetic field due to a long straight current-carrying wire at a distance \( r \) from the wire is given by:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
Where:
- \( B \) is the magnetic field.
- \( \mu_0 \) is the permeability of free space (\( 4\pi \times 10^{-7} \) T·m/A).
- \( I \) is the current.
- \( r \) is the distance from the wire to the point in question.
The directions of the magnetic fields created by each wire can be determined using the right-hand rule.
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