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Minimize Flux Rectangular Coil A rectangular coil in the plane of the page has dimensions a = 1 m and b = 35 m. A long wire that carries a current I = 4.5 A is placed directly above the coil. For what value of x is the magnitude of the magnetic flux through the coil a minimum? O a

Minimize Flux Rectangular Coil A rectangular coil in the plane of the page has dimensions a = 1 m and b = 35 m. A long wire that carries a current I = 4.5 A is placed directly above the coil. For what value of x is the magnitude of the magnetic flux through the coil a minimum? O a

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In this problem Iam supposed to find length x how am I supposed to approach this.

**Minimize Flux Rectangular Coil** A rectangular coil in the plane of the page has dimensions \( a = 1 \, \text{m} \) and \( b = 35 \, \text{m} \). A long wire that carries a current \( I = 4.5 \, \text{A} \) is placed directly above the coil. For what value of \( x \) is the magnitude of the magnetic flux through the coil a minimum? --- In the diagram accompanying the text, a rectangular coil is depicted. The coil is positioned in the plane of the page with sides labeled as \( a \) and \( b \). The length \( a \) (1 m) is horizontal, and the length \( b \) (35 m) is vertical. A long horizontal wire is situated above the coil, carrying a current denoted as \( I = 4.5 \, \text{A} \). The distance \( x \) is the vertical distance from the wire to the top edge of the coil, and it is also indicated as the variable to be minimized for the magnetic flux through the coil. There is also a small text box at the bottom labeled \( x = \) for inputting the value of \( x \).
Transcribed Image Text:**Minimize Flux Rectangular Coil** A rectangular coil in the plane of the page has dimensions \( a = 1 \, \text{m} \) and \( b = 35 \, \text{m} \). A long wire that carries a current \( I = 4.5 \, \text{A} \) is placed directly above the coil. For what value of \( x \) is the magnitude of the magnetic flux through the coil a minimum? --- In the diagram accompanying the text, a rectangular coil is depicted. The coil is positioned in the plane of the page with sides labeled as \( a \) and \( b \). The length \( a \) (1 m) is horizontal, and the length \( b \) (35 m) is vertical. A long horizontal wire is situated above the coil, carrying a current denoted as \( I = 4.5 \, \text{A} \). The distance \( x \) is the vertical distance from the wire to the top edge of the coil, and it is also indicated as the variable to be minimized for the magnetic flux through the coil. There is also a small text box at the bottom labeled \( x = \) for inputting the value of \( x \).
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