A high voltage power line carries a current of 110 A at a location where the Earth's magnetic fields has a magnitude of 5.9 x 10^-4 T and points north at an angle of72 degrees below the horizontal (toward the earth surface). Find the direction and magnitude of the magnetic force exerted on a 250m length of wire if the wire flows
a) horizontally toward the east
b) horizontally toward the south
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To find the magnitude and direction of the magnetic force exerted on the wire, we can use the formula for the magnetic force on a current-carrying wire:
F = I * L * B * sin(θ)
where:
F = magnetic force
I = current through the wire
L = length of the wire
B = magnetic field strength
θ = angle between the current direction and the magnetic field direction
a) If the wire flows horizontally toward the east:
In this case, the angle between the current direction and the magnetic field direction is 90 degrees, because the magnetic field is pointing north and the wire is flowing east. The sine of 90 degrees is 1.
Using this information, we can calculate the magnetic force:
F = (110 A) * (250 m) * (5.9 x 10^-4 T) * sin(90°)
F = 16.775 N
The magnetic force has a magnitude of 16.775 N and it is directed vertically upward.
b) If the wire flows horizontally toward the south:
In this case, the angle between the current direction and the magnetic field direction is 162 degrees (180 degrees minus 72 degrees). The sine of 162 degrees is -0.9397.
Using this information, we can calculate the magnetic force:
F = (110 A) * (250 m) * (5.9 x 10^-4 T) * sin(162°)
F = -17.598 N
The magnetic force has a magnitude of 17.598 N and it is directed vertically downward.
To find the direction and magnitude of the magnetic force exerted on a wire carrying a current in a magnetic field, we can use the right-hand rule for magnetic forces.
Before we apply the right-hand rule, let's define some variables:
I = Current flowing through the wire = 110 A
B = Magnetic field strength = 5.9 x 10^-4 T
L = Length of the wire = 250 m
a) Horizontally toward the east:
Using the right-hand rule, we can determine the direction of the magnetic force by using our right hand. In this case, point your thumb in the direction of the current flow (east) and your fingers in the direction of the magnetic field (north).
The force will be directed in a direction perpendicular to both the current direction and the magnetic field direction. In this case, the force will be directed upward.
Now, to find the magnitude of the force, we can use the formula:
F = BIL sinθ
Where θ is the angle between the current direction and the magnetic field direction. In this case, θ is 72 degrees below the horizontal, so sinθ = sin(72°) = 0.951.
Plugging in the values, we have:
F = (5.9 x 10^-4 T) * (110 A) * (250 m) * (0.951)
F ≈ 15.31 N
Therefore, the magnitude of the magnetic force exerted on the wire flowing horizontally toward the east is approximately 15.31 N, directed upward.
b) Horizontally toward the south:
Using the right-hand rule, point your thumb in the direction of the current (south) and your fingers in the direction of the magnetic field (north). The force will be directed downward.
Using the same formula:
F = BIL sinθ
Since the angle θ is still 72 degrees, θ is above the horizontal this time, we need to use sin(180° - θ) instead of sinθ. In this case, sin(180° - 72°) = sin(108°) = 0.951.
Plugging in the values, we have:
F = (5.9 x 10^-4 T) * (110 A) * (250 m) * (0.951)
F ≈ 15.31 N
Therefore, the magnitude of the magnetic force exerted on the wire flowing horizontally toward the south is approximately 15.31 N, directed downward.