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!

 

[rwisz]

I would like to clarify that the direction of the magnetic field in this scenario depends on the orientation of the wire and the direction of the current. The direction of the magnetic force acting on a current-carrying wire is given by the right-hand rule, where the thumb points in the direction of the current, the fingers point in the direction of the magnetic field, and the palm indicates the direction of the force.

In the figure provided, the current is flowing upwards in the wire (in the +y direction), which means the magnetic field must be oriented in the -y direction in order for the force to be maximum. This is because the force is perpendicular to both the current and the magnetic field, and in order for the force to be maximum, the current and the magnetic field must be at a 90 degree angle to each other.

Therefore, the key is correct in stating that the direction of the magnetic field in this scenario is -y. It is important to keep in mind that the direction of the magnetic field is always perpendicular to the direction of the current and the direction of the force. So, depending on the orientation of the wire and the direction of the current, the direction of the magnetic field can change.