Aluminum has a density of 2.7x103 kg/m3 . A 3.0-cm long straight segment of cyli

Question

Aluminum has a density of 2.7x103 kg/m3 . A 3.0-cm long straight segment of cylindrical aluminum wire is seen floating horizontally above the ground where the Earth’s magnetic field is 5.0x10-5 T pointing directly north. (Dip angle = 0.) The wire has a diameter of 2.0 mm. A current I exists in the wire. Assuming that the only forces acting on the wire are gravity and magnetism. What are the magnitude of and direction of the magnetic force?

a) What is the minimum current needed in the wire to produce that magnetic force?

b) What current direction, and thus the direction of the wire, corresponds to the condition of minimum required current?

Explanation / Answer

rho = 2700 kg/m^3
l = 0.03m
r = 0.001m
A= pir^2
m = rholA = 2700*0.03*3.14*0.001^2 = 0.025434 kg
mg = 0.2492 N

Magnetic force = mg = 0.2492 N
Direction = opposite to gravity = upwards

a) F = BILsin(theta) = BIL = 5*10^-5 * I * 0.03 = 0.2492
I = 1.6616 * 10 ^5 A
b) Direction = towards east [from left hand rule]

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