A question about the point of action of the magnetic force

In summary, the conversation discusses the translation of extended objects and the computation of rotational motion. It also presents an example of a loop with a current and a magnetic field, resulting in a torque causing rotation around the Y axis. The conversation raises the question of how to prove the force distribution responsible for the torque, with one force acting on the first quadrant and the other on the second quadrant. It is suggested to think of the force as distributed around the entire loop and to use mathematical models to show the relationship between the force and the position of the loop's segments. This can then be replaced by an equivalent couple.
  • #1
sergioro
8
0
Hello everyone,

Translation of extended objects is described taking the
net force acting on the center of mass of the extended object.
But to compute rotational motion, one needs to considers
each force on their point of action.

For example, let's consider a current I flowing in a loop consisting of
a conductor forming a semicircle and another as a straight segment
trough the diameter of the semicircle. Assume the current flows
counterclockwise in the loop which lies on the XY plane (being the semicircle part on the
+Y-axis) and that a constant magnetic field in the +X direction is acting on the loop.

In this situation a torque will make the loop to rotate around the
Y axis.

How can one prove that the forces responsible of the torque, one acts
at the mid point of the piece of the curved loop in the first
quadrant and the other at the mid point of the piece of the curved loop
in the second quadrant?

Thanks in advance,

Sergio
 
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  • #2
The fact there is a measurable torque is the proof of the force distribution you talk about ... but you should think of the force as distributed around the entire loop - not acting at a single point.

Mathematically you can show this is consistent with current models by dividing the loop into very short segments which can be treated as if they are straight, much like we often treat the ground as flat, and then applying the rule for a current in a straight wire for each segment... find the relationship between the position of the segment in the loop with the force on the section.

We can replace the distributed force by an equivalent couple that works like you describe.
 
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  • #3
Thanks, Simon. The first part of your comment triggers the intuition I was missing.
 
  • #4
NO worries - that's what I'm here for.
 
  • #5


I would like to clarify that the point of action of the magnetic force is the point at which the force is applied on an object. In the example given, the magnetic force is acting on the loop in the +X direction, causing a torque that makes the loop rotate around the Y axis. To prove that the forces responsible for this torque act at the midpoints of the curved loop in the first and second quadrants, we can use the principles of vector addition and the right-hand rule. By breaking down the magnetic force into its components and considering the direction of rotation, we can determine that the forces acting at the midpoints of the loop are perpendicular to the radius of the loop, thus producing a torque. This can be further supported by mathematical calculations using the principles of torque and rotational motion. I hope this helps clarify the concept of the point of action of the magnetic force.
 

1. What is the point of action of the magnetic force?

The point of action of the magnetic force is the location where the magnetic field is exerting a force on a charged particle or a magnet. This force is perpendicular to both the direction of the magnetic field and the velocity of the charged particle.

2. How is the point of action of the magnetic force determined?

The point of action of the magnetic force is determined by the direction of the magnetic field and the velocity of the charged particle or magnet. It is also dependent on the strength of the magnetic field and the charge or magnetic moment of the particle or magnet.

3. Can the point of action of the magnetic force change?

Yes, the point of action of the magnetic force can change if the direction or strength of the magnetic field changes, or if the velocity or charge/magnetic moment of the particle or magnet changes. It can also change if the distance between the particle or magnet and the source of the magnetic field changes.

4. What is the significance of the point of action of the magnetic force?

The point of action of the magnetic force is significant because it determines the direction and magnitude of the force exerted on a charged particle or magnet by the magnetic field. It is also important in understanding the behavior of magnetic materials and in applications such as electric motors and generators.

5. How does the point of action of the magnetic force relate to the Lorentz force?

The point of action of the magnetic force is a key component of the Lorentz force, which describes the force exerted on a charged particle by an electric and magnetic field. The cross product of the velocity and magnetic field vectors determines the direction of the force, and the distance between the particle and the magnetic field source determines the magnitude of the force.

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