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

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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 adds that these forces must lie along the line connecting the particles. There are scenarios, such as magnetic forces acting on moving charges, where both forms can fail. In these cases, the weak form may still hold, as forces can be equal and opposite but not collinear. An example includes a charge near a magnet, where the forces are perpendicular to the relevant directions. Understanding these distinctions is crucial for analyzing force interactions in various physical contexts.
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[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

 
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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.
 
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