The mass per unit length of a 14-gauge copper wire is 18.5 g/m. If the wire is placed running along the horizontal x-axis (east-west) in a region in which there is a uniform 0.288-T magnetic field directed along the horizontal y-axis (northward). Calculate the magnitude of the minimum current in the wire that could allow the wire to levitate if the conventional current points to the east.

The magnitude of the minimum current in the wire that will allow the wire to levitate if the conventional current points to the east, is 0.63 A.

The given parameters;

mass per unit length of the copper wire, m/L = 18.5 g/m
magnetic field strength, B = 0.288 T

The magnitude of the minimum current in the wire that will allow the wire to levitate if the conventional current points to the east, is calculated as;

[tex]F = BIL\ sin(\theta)\\\\mg = BIL \ sin(90)\\\\mg = BIL\\\\I = \frac{mg}{BL} \\\\I = (\frac{m}{L} ) \times \frac{g}{B} \\\\I = (0.0185) \times \frac{9.8}{0.288} \\\\I = 0.63 \ A[/tex]

Thus, the magnitude of the minimum current in the wire that will allow the wire to levitate if the conventional current points to the east, is 0.63 A.

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