Magnetic Force on a Current Carrying Wire

[taliaroma]

The figure shows a current i through a wire in a uniform magnetic field , as well as the magnetic force acting on the wire. The field is oriented so that the force is maximum. In what direction is the field?

I have uploaded the figure, and the relevant equations.

My reasoning:
-L is in the direction of i.
-Assume i is a positive value.
Therefore, B is in the direction of +y.

However, the key says the answer is -y.

Why is that?

 

[PsychoDash]

You're doing the right hand rule incorrectly. Your thumb needs to be pointing in the direction of the magnetic force. When you do this and orient your fingers to point in the direction of i in the picture, you will see that they curl down, in the -y direction.

 

[sona1177]

The figure shows a current i through a wire in a uniform magnetic field , as well as the magnetic force acting on the wire. The field is oriented so that the force is maximum. In what direction is the field?

I have uploaded the figure, and the relevant equations.

My reasoning:
-L is in the direction of i.
-Assume i is a positive value.
Therefore, B is in the direction of +y.

However, the key says the answer is -y.

Why is that?

Homework Statement

Homework Equations

The Attempt at a Solution

Think about it this way:

What has to be the orientation of L and B in order for the force to be the maximum? What does theta have to be? I am assuming you understand that it is perpendicular since you narrowed it down to the y direction. Now you have two choices, either the + y direction or the - y direction. Assuming you have a positive charge and the force is out of the page in z direction (thumb points out of the page, fingers point in direction of current towards left, -x direction, now which way do your fingers naturally naturally curl?). This is the direction of the magnetic field (assuming its not changing and is uniform). Does that make sense?

 

[taliaroma]

Think about it this way:

What has to be the orientation of L and B in order for the force to be the maximum? What does theta have to be? I am assuming you understand that it is perpendicular since you narrowed it down to the y direction. Now you have two choices, either the + y direction or the - y direction. Assuming you have a positive charge and the force is out of the page in z direction (thumb points out of the page, fingers point in direction of current towards left, -x direction, now which way do your fingers naturally naturally curl?). This is the direction of the magnetic field (assuming its not changing and is uniform). Does that make sense?

Yes, that's very helpful. Thank you!