At New York City, the earth's magnetic field has a vertical component of that points downward (perpendicular to the ground) and a horizontal component of that points toward geographic north (parallel to the ground). What are the magnitude and direction of the magnetic force on a 6.0-m long, straight wire that carries a current of perpendicularly into the ground?
3.78x10^-3N
To determine the magnitude and direction of the magnetic force on a straight wire carrying a current in New York City, we can use the right-hand rule for determining the direction of the magnetic field and the right-hand rule for determining the direction of the magnetic force.
First, let's find the magnitude of the magnetic field produced by the wire. We can use the formula for the magnetic field produced by a current-carrying wire:
B = (μ₀/2π) * (I/r)
Where:
B is the magnetic field,
μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A),
I is the current,
r is the distance from the wire.
Given that the wire carries a current of I = ??? A (the value is missing in the question), we need to assume a value in order to proceed with the calculation. Let's assume I = 1 A for simplicity.
Next, we need to determine the direction of the magnetic field. The question states that the vertical component of the Earth's magnetic field points downward, while the horizontal component points toward geographic north.
Since the wire carries a current perpendicularly into the ground, the magnetic field produced will be parallel to the wire and perpendicular to the plane of the ground. Therefore, the magnetic field will be horizontal and point toward geographic north.
Now, using the right-hand rule for determining the direction of the magnetic force, we can determine the direction of the force on the wire.
If you point your right thumb in the direction of the current (perpendicular into the ground), and curl your fingers, the direction in which your fingers curl will indicate the direction of the magnetic force on the wire.
Finally, to calculate the magnitude of the magnetic force on the wire, we can use the formula:
F = |I| * |B| * L
Where:
F is the magnetic force,
|I| is the magnitude of the current,
|B| is the magnitude of the magnetic field,
L is the length of the wire.
Given that the wire is 6.0 m long (L = 6.0 m), we can substitute the values for |I|, |B|, and L into the formula and calculate the magnitude of the magnetic force.