Do all cases of Newton's third law follow both the strong and weak forms?

Click For Summary
SUMMARY

Newton's Third Law has two forms: the Weak Form states that forces between two particles are equal in magnitude and opposite in direction, while the Strong Form requires these forces to also lie on the line connecting the particles. Cases exist where both forms fail, particularly in magnetic interactions. For instance, magnetic forces acting on a moving charge in a magnetic field obey the Weak Form but not the Strong Form, as the forces are not collinear. This discussion clarifies the conditions under which these laws apply and highlights specific examples involving magnetic forces.

PREREQUISITES
  • Understanding of Newton's Laws of Motion
  • Familiarity with magnetic forces and their mathematical representation
  • Basic knowledge of vector forces and their properties
  • Concept of electric charges and their interactions
NEXT STEPS
  • Study the mathematical representation of magnetic forces on moving charges
  • Explore the implications of non-collinear forces in physics
  • Investigate scenarios where Newton's Third Law may not apply
  • Learn about the relationship between electric currents and magnetic fields
USEFUL FOR

Physics students, educators, and anyone interested in the nuances of classical mechanics and the application of Newton's laws in various physical scenarios.

ehrenfest
Messages
2,001
Reaction score
1
[SOLVED] Newton's third law

Homework Statement


My book gives two forms of Newton's Third Law:
Weak Form: The forces exerted by two particles \alpha and \beta on each other are equal in magnitude and opposite in direction
Strong Form: The forces exerted by two particles \alpha and \beta on each other, in addition to being equal and oppositive, must lie on the straight line joining the two particles.

Here are my questions:
1) Is it true that there are cases IN WHICH BOTH THE STRONG FORM AND THE WEAK FORM FAIL TO HOLD?
2) My book says that for example, magnetic forces, those forces exerted on a moving charge q in a magnetic field \mathbf{B} (\mathbf{F}=\mathbf{q}v \times \mathbf{B}), obey the weak form, but not the strong form. I don't understand why that obeys the weak form. What are the two particles?

Homework Equations


The Attempt at a Solution

 
Last edited:
Physics news on Phys.org
1.
Consider two identical charges moving along the x and y axes with same speed away from the origin. The electrical forces between them is repulsive, but now just find out how the magnetic forces between them behave. You don't have to calculate -- just roughly think of the charges as currents and find the direction of the associated magnetic fields like we do for currents.

The total force of one on the other is equal to the force of the other on the former, but they are not opposite. So, this violates both weak and strong.

2.
Consider one charge and the wire in which current is flowing that makes the magnetic field B. Or simply a magnet and a charge near one of the poles, moving in a direction perpendicular to the axis of the magnet. The force on the charge is perpendicular to the plane containing B and v. The force on the magnet is opposite, but not collinear. So, the weak form holds.
 
Last edited:

Similar threads

Replies
5
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 25 ·
Replies
25
Views
2K
  • · Replies 23 ·
Replies
23
Views
5K
Replies
6
Views
1K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 28 ·
Replies
28
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 14 ·
Replies
14
Views
1K
Replies
6
Views
2K