Moving wires in magnetic field/force

[pujam3]

Homework Statement

A long straight wire 1 lies along the x-axis. A long straight wire 2 lies along the y-axis so as
to pass very near, but not quite touch wire 1 at the origin. If both wires are free to move, what happens when currents are sent simultaneously in the +x direction through wire 1 and in the +y direction through wire 2? Note that “clockwise around origin” refers to an observer looking down on an xy plane in which +x is to the right and +y upward.

1. Both wires accelerate along the direction of current flow.
2. 1 accelerates in the −y direction, 2 in the -x direction.
3. Both wires rotate counterclockwise around the origin.
4. 1 accelerates in the +y direction, 2 in the -x direction.
5. Neither wire moves.
6. 1 accelerates in the +y direction, 2 in the +x direction.
7. 1 rotates counterclockwise, 2 clockwise around the origin.
8. 1 accelerates in the −y direction, 2 in the +x direction.
9. Both wires rotate clockwise around the origin.
10. 1 rotates clockwise, 2 counterclockwise around the origin.

Homework Equations

None

The Attempt at a Solution

I tried using the Right hand rule (#1) to find out the direction of the magnetic field on both wires, then i used the Right hand rule (#2) to find out the direction of the force to find out how it would move. I ended up getting wire 1 moving into the page, which doesn't seem right and is not in one of the answer choices.

 

[pujam3]

Nevermind, Solved.

 

[nlightner]

I would like to address this question by first clarifying that the movement of wires in a magnetic field is governed by the principles of electromagnetism, specifically the Lorentz force law. This law states that a current-carrying wire in a magnetic field will experience a force perpendicular to both the direction of the current and the magnetic field.

In this scenario, both wires are carrying a current and are placed in close proximity to each other, creating a magnetic field. When currents are sent through both wires simultaneously, the Lorentz force law will apply to both wires. The direction of the force on each wire will depend on the direction of the current and the direction of the magnetic field.

Using the right hand rule, we can determine the direction of the magnetic field created by wire 1 on wire 2. Since wire 1 is carrying a current in the +x direction, the magnetic field will be perpendicular to the wire and will point in the +z direction (out of the page). Similarly, the magnetic field created by wire 2 on wire 1 will point in the -z direction (into the page).

Now, to determine the direction of the force on each wire, we need to consider the direction of the current and the direction of the magnetic field. For wire 1, the current is flowing in the +x direction and the magnetic field is pointing in the -z direction. Using the right hand rule, we can see that the force on wire 1 will be in the +y direction, causing it to accelerate in that direction (#4). For wire 2, the current is flowing in the +y direction and the magnetic field is pointing in the +z direction. This will result in a force in the -x direction, causing wire 2 to accelerate in that direction (#2).

It is also important to note that since both wires are experiencing a force in opposite directions, they will also experience a torque around the origin. This will cause both wires to rotate counterclockwise around the origin (#3).

In conclusion, the correct answer to this question is #4 - wire 1 accelerates in the +y direction and wire 2 accelerates in the -x direction, with both wires rotating counterclockwise around the origin. This is in accordance with the principles of electromagnetism and the Lorentz force law.