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.

I recall answering this yesterday. I left the final steps for you to do. Please check your previous post.

The answer requires multiplying B (the magnetic field), I (current), L (wire length) and the sine of 56 degrees, the angle between the current and the B vectors

how can we do the B part of the question...

B) If the current is horizontal to the east, and the B field remains inclined 34 degrees to verical, pointed north, B and I are perpendicular. The force is B I L without any sine or cosine factor. The direction of the force will be perpendicular to both, in the north-south vertical plane, but inclined upward 34 degrees from the horizon plane of the earth. Use the right-hand rule when forming I x B

A) To find the magnitude and direction of the force on the wire when the current is flowing horizontally to the North, we can use the right-hand rule for the magnetic force on a current-carrying wire.

1. Determine the direction of the magnetic field: The magnetic field is given as 5 * 10^(-5) T and points North, 34 degrees from the vertical axis. This means it is inclined 34 degrees from the vertical axis towards the North.

2. Draw the "North-vertical" plane: Draw a two-dimensional plane with the North direction vertically upwards and the vertical axis perpendicular to it.

3. Orient your hand: Place your right hand so that the thumb points towards the North, your palm faces downward, and your fingers are extended towards the vertical axis.

4. Align the wire with your fingers: Point your fingers in the direction of the current, which is horizontally to the North.

5. Use your thumb to find the force direction: When you align your fingers with the current and your thumb with the magnetic field, your thumb will indicate the direction of the force. In this case, your thumb will point towards the West.

6. Determine the magnitude of the force: To calculate the magnitude of the force, we use the formula F = BIL, where F is the force, B is the magnetic field, I is the current, and L is the length of the wire. Plugging in the given values, we get F = (5 * 10^(-5) T) * (105 A) * (175 m) = 0.91875 N

Therefore, the magnitude of the force is approximately 0.92 N, and the direction of the force is towards the West.

B) To find the magnitude and direction of the force on the wire when the current is flowing horizontally to the east, we need to repeat the previous steps, considering the new direction of the current.

1. Orient your hand: Place your right hand so that the thumb points towards the North, your palm faces downward, and your fingers are extended towards the vertical axis.

2. Align the wire with your fingers: Point your fingers in the direction of the current, which is now horizontally to the East.

3. Use your thumb to find the force direction: When you align your fingers with the current and your thumb with the magnetic field, your thumb will indicate the direction of the force. In this case, your thumb will point towards the East.

4. Determine the magnitude of the force: Using the same formula F = BIL, with the given values, we get F = (5 * 10^(-5) T) * (105 A) * (175 m) = 0.91875 N.

Therefore, the magnitude of the force is approximately 0.92 N, and the direction of the force is towards the East.