1₁ = 6.00 A 1₂ = 3.00 A I = ? left 1₂ = 9.00 A upward right downward Four very long, current-carrying wires in the same plane intersect to form a square 30.0 cm on each side, as shown in the figure. Find the magnitude and direction of the current I so that the net magnetic field at the center of the square is 4.00 x 106 T and out of the page.
1₁ = 6.00 A 1₂ = 3.00 A I = ? left 1₂ = 9.00 A upward right downward Four very long, current-carrying wires in the same plane intersect to form a square 30.0 cm on each side, as shown in the figure. Find the magnitude and direction of the current I so that the net magnetic field at the center of the square is 4.00 x 106 T and out of the page.
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Transcribed Image Text:### Magnetic Field Calculation in a Square Configuration of Current-Carrying Wires
In this diagram, we have a configuration where four long, current-carrying wires form a square with each side measuring 30.0 cm. The wires carry the following currents:
- \(I_1 = 6.00 \, \text{A}\) (downward)
- \(I_2 = 3.00 \, \text{A}\) (downward)
- \(I_3 = 9.00 \, \text{A}\) (to the left)
- \(I = ?\) (unknown direction and magnitude)
The problem requires determining the current \(I\) such that the net magnetic field at the center of the square is \(4.00 \times 10^{-6} \, \text{T}\) directed out of the page.
#### Diagram Explanation
The diagram shows the square configuration with arrows indicating the direction of each current. The directions for positive directions are:
- Upward
- Downward
- Left
- Right
#### Multiple Choice Options
The possible magnitudes and directions for the current \(I\) are:
- \( 15.0 \, \text{A, to the right} \)
- \( 18.0 \, \text{A, to the left} \)
- \( 3.00 \, \text{A, to the right} \)
- \( 18.0 \, \text{A, to the right} \)
- \( 6.00 \, \text{A, to the left} \)
- \( 6.00 \, \text{A, to the right} \)
- \( 9.00 \, \text{A, to the left} \)
- \( 9.00 \, \text{A, to the right} \)
- \( 3.00 \, \text{A, to the left} \)
- \( 15.0 \, \text{A, to the left} \)
The objective is to calculate the appropriate magnitude and direction for \( I \) so that the conditions of the net magnetic field are satisfied.
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