# Forms of Newton's third law

1. Feb 14, 2008

### ehrenfest

[SOLVED] Newton's third law

1. The problem statement, all variables and given/known data
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?
2. Relevant equations

3. The attempt at a solution

Last edited: Feb 14, 2008
2. Feb 14, 2008

### Shooting Star

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: Feb 14, 2008