A high-voltage power line carries a current of 120 A at a location where the Earth's magnetic field has a magnitude of 0.577 G and points to the north, 70.8° below the horizontal. Calculate the magnitude of the magnetic force exerted on a 258 m length of wire if the current in the wire flows horizontally toward the east.
Calculate the magnitude of the magnetic force exerted on a 258 m length of wire if the current in the wire flows horizontally toward the south.
To calculate the magnitude of the magnetic force exerted on the wire, you can use the formula:
F = BILsin(θ)
where:
F is the magnetic force
B is the magnetic field strength
I is the current in the wire
L is the length of the wire
θ is the angle between the magnetic field direction and the current direction.
First, let's calculate the magnitude of the magnetic force when the current flows horizontally towards the east:
Given:
Current, I = 120 A
Length, L = 258 m
Magnetic field strength, B = 0.577 G = 0.577 x 10^-4 T (since 1 G = 10^-4 T)
The angle between the magnetic field and the current direction is 90 degrees when flowing horizontally.
θ = 90°
Plugging the values into the formula, we have:
F = (0.577 x 10^-4 T) * (120 A) * (258 m) * sin(90°)
The sin(90°) term will give us 1, so the equation simplifies to:
F = (0.577 x 10^-4 T) * (120 A) * (258 m) * 1
Calculating the values, we get:
F = 0.448 N
Therefore, the magnitude of the magnetic force exerted on the wire when the current flows horizontally towards the east is 0.448 N.
Now, let's calculate the magnitude of the magnetic force when the current flows horizontally towards the south:
The angle between the magnetic field and the current direction is now 160.8 degrees (90 degrees for horizontal and 70.8 degrees below the horizontal).
θ = 160.8°
Plugging the values into the formula, we have:
F = (0.577 x 10^-4 T) * (120 A) * (258 m) * sin(160.8°)
Calculating the values, we get:
F = 0.630 N
Therefore, the magnitude of the magnetic force exerted on the wire when the current flows horizontally towards the south is 0.630 N.