Wednesday, March 21, 2012

Paradoxical Lorentz force internal to a triangle coil




Take a rigid triangle coil (Fixed on a wooden plate, yellow in the Figure 1), a current I flows in it. The 3 sides would feel a Lorentz force from the magnetic field of the other sides. These force are internal to the coil.

Now, put the side s3 inside a ideal magnetic shield. So, the sides s1 and s2 would not feel the magnetic field from the side s3 and the latter does not feel that from s1 and s2. What will be the total internal force on the triangle in this case?

The side s3 would feel no force. The side s1 would feel the Lorentz force F1 from the side s2 and the side s2 the Lorentz force F2 from s1 respectively. So, the total internal force of the triangle coil is F3= F1+F2. As the forces F1 and F2 are Lorentz forces, they are perpendicular to their sides and they make an angle between them. Their resultant force F3 is non null.

If the total internal force is non null, any movement in the direction of the resultant force would do a work and create a energy. This is impossible because energy cannot be created.

So, the fact that the Lorentz force is perpendicular to the current violates the third Newton's law and the energy conservation law. This is the paradox of the internal Lorentz force.

This paradox is explained and solved in the document behind the link Paradoxes and Solutions.



The Lorentz force law presents some deficiencies. A study is in this document..
Paradoxes and Solutions

No comments:

Post a Comment