A high-voltage line of length 175 m is carrying a current of 105 A at a point on the earth where its magnetic field is 5 * 10^(-5) T and points North,34 degree from the vertical axis.
A) what is the magnitude and direction of the force on the wire if the current is flowing horizontally to the North?
HINT: horizontal is 90 degree from the vertical axis. Also, it may keep your brain from hurting too much by drawing the two dimensional "North- vertical" plane.
B)What is the magnitude and direction of the force on the wire if the current is flowing horizontally to the east?
Hint: Again the North-vertical plane is your friend.
The force is the cross product of
I X B times the length of the wire. The force acts perpendicular to the plane containing the wire and the B vector. This is the north-south vertical plane. Therefore the force is is towards the east. Its magnitude is
F = I B sin 56. The sine of the angle between the vectors (90 - 34 degrees in this case) always shows up in the cross product.
SO what is the force for the second question..
A) To determine the magnitude and direction of the force on the wire when the current is flowing horizontally to the North, we can use the formula for the magnetic force on a current-carrying wire:
F = I * L * B * sin(θ)
Where:
F is the force on the wire
I is the current flowing through the wire
L is the length of the wire
B is the magnetic field
θ is the angle between the current direction and the magnetic field direction
1. Calculate the magnitude of the force:
F = 105 A * 175 m * 5 * 10^(-5) T * sin(34°)
2. Calculate the direction of the force:
The direction of the force can be determined using the right-hand rule. Point your thumb in the direction of the current (North) and your fingers in the direction of the magnetic field (vertical). Your palm will indicate the direction of the force.
B) Similarly, to determine the magnitude and direction of the force on the wire when the current is flowing horizontally to the east:
1. Calculate the magnitude of the force by using the formula from above:
F = 105 A * 175 m * 5 * 10^(-5) T * sin(90°)
2. Calculate the direction of the force using the right-hand rule:
Point your thumb in the direction of the current (east) and your fingers in the direction of the magnetic field (vertical). Your palm will indicate the direction of the force.
By following these steps, you can calculate the magnitude and direction of the force on the wire for both scenarios.