A straight 25.0-g wire that is 1.80 m long carries a current of 6/30 A. This wire is aligned horizontally along the west-east direction with the current going from west to east. You want to support the wire against gravity using the weakest possible uniform external magnetic field. (a) Which way should the magnetic field point?(b) What is the magnitude of the weakest possible magnetic field you could use?

a) The magnetic field should point upwards(i.e the north)

b) The magnitude of the weakest possible magnetic field is 0.681 Tesla

Explanation:

a) Since the force of gravity is acting vertically downwards, for equilibrium to be maintained, the force due to the magnetic field should act upwards in the north direction. since F = I (LXB), and the aim is to obtain a maximum LXB using the weakest possible magnetic field, according to the right hand rule, the magnetic field must point in the morth direction (i.e upwards) to maintain a balance between gravity and force due to magnetic field.

b) mass, m = 25.0g = 25 * 10⁻³kg

Length, L = 1.8m

Current, I = 6/30 A

g = 9.8 m/s²

F = mg(1)

F = ILB(2)

Equating (1) and (2)

mg = ILB

B = mg/IL

B = (25 * 10⁻³*9.8)/(6/30  *  1.8)

B = 0.245/0.36

B = 0.681 Tesla

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