Final answer:
To determine the magnitude of the current passing through the copper wire that floats horizontally in air due to Earth's magnetic field, we can equate the magnetic force to the weight of the wire. By using relevant formulas and calculations, the magnitude of the current is determined to be approximately 8.23 A.
Step-by-step explanation:
To determine the magnitude of the current passing through the copper wire, we can use the equation for the magnetic force experienced by a current-carrying wire in a magnetic field:
F = BIL,
where F is the magnetic force, B is the magnetic field, I is the current, and L is the length of the wire.
Given that the wire is able to "float" horizontally in air due to the force from the Earth's magnetic field (B = 6.2×10−5 T), we can equate the magnetic force to the weight of the wire:
F = mg,
where m is the mass and g is the acceleration due to gravity.
From the diameter of the wire (1.40 mm), we can calculate its mass using the formula for the volume of a cylinder:
m = πr²Lρ,
where r is the radius of the wire, L is its length, and ρ is the density of copper.
Plugging in the values and solving for I, we get:
I = mg/(BL).
Calculating the values and substituting them into the equation, the magnitude of the current passing through the wire is approximately: 8.23 A.