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The figure shows a 1.59-m long semicircular wire segment carrying a 5.6-A current in the xy-plane immersed in a uniform 1.1-T magnetic field. Calculate the magnetic force magnitude on the wire segment. B ONL L.

The figure shows a 1.59-m long semicircular wire segment carrying a 5.6-A current in the xy-plane immersed in a uniform 1.1-T magnetic field. Calculate the magnetic force magnitude on the wire segment. B ONL L.

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The figure illustrates a 1.59-meter long semicircular wire segment that carries a current of 5.6 Amperes in the xy-plane. The wire is placed in a uniform magnetic field with a strength of 1.1 Tesla. The task is to calculate the magnitude of the magnetic force on the wire segment. ### Diagram Description: - The semicircular wire is depicted in gold/orange. - The direction of the current (I) is indicated by a red arrow along the semicircle, traveling counterclockwise. - The magnetic field (\(\vec{B}\)) is represented by blue dots indicating that the field vector is directed out of the page. - An xy coordinate system is included for reference, with the semicircle lying in this plane. To calculate the magnetic force, use the formula for the magnetic force on a current-carrying wire: \[ F = I \cdot L \cdot B \cdot \sin(\theta) \] Here: - \( F \) is the magnetic force. - \( I \) is the current (5.6 A). - \( L \) is the length of the wire in the direction of the magnetic field. - \( B \) is the magnetic field strength (1.1 T). - \( \theta \) is the angle between the current direction and the magnetic field vector. For a semicircle, the effective length is the straight-line distance (diameter), and the force calculation considers the perpendicular component of the field. The semicircular configuration requires integration over the path or application of symmetries, factoring in that the net force will only consider the component along the line segment substituting L with the full diameter due to symmetry along the y-axis.
Transcribed Image Text:The figure illustrates a 1.59-meter long semicircular wire segment that carries a current of 5.6 Amperes in the xy-plane. The wire is placed in a uniform magnetic field with a strength of 1.1 Tesla. The task is to calculate the magnitude of the magnetic force on the wire segment. ### Diagram Description: - The semicircular wire is depicted in gold/orange. - The direction of the current (I) is indicated by a red arrow along the semicircle, traveling counterclockwise. - The magnetic field (\(\vec{B}\)) is represented by blue dots indicating that the field vector is directed out of the page. - An xy coordinate system is included for reference, with the semicircle lying in this plane. To calculate the magnetic force, use the formula for the magnetic force on a current-carrying wire: \[ F = I \cdot L \cdot B \cdot \sin(\theta) \] Here: - \( F \) is the magnetic force. - \( I \) is the current (5.6 A). - \( L \) is the length of the wire in the direction of the magnetic field. - \( B \) is the magnetic field strength (1.1 T). - \( \theta \) is the angle between the current direction and the magnetic field vector. For a semicircle, the effective length is the straight-line distance (diameter), and the force calculation considers the perpendicular component of the field. The semicircular configuration requires integration over the path or application of symmetries, factoring in that the net force will only consider the component along the line segment substituting L with the full diameter due to symmetry along the y-axis.
Expert Solution
Step 1: Formula

The magnetic force acting on a semi-circular current carrying wire kept in a uniform magnetic field perpendicular to the plane of the wire is 

F equals 2 B I R

Here, 

B is the magnetic field, 

I is the current 

R is the radius

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