# Magnetic Field Due To Moving Charges: An Unsound Conclusion?

1. Aug 1, 2007

### Sleek

1. The problem statement, all variables and given/known data
This is not exactly a homework problem, but something extra posed to me by one of my friends, who seems to have derived a rather confusing conclusion.

A diagram (which they had) and I've reproduced precisely is given below.

q1 and q2 are two charges, v1 and v2 being their respective velocities. The line connecting the two charge (r) is what they call the radius vector.

2. Relevant equations

$$B=v \times \frac{E}{c^2}$$ (Biot-Savart's Law)

3. The attempt at a solution

They first consider the charge q1 and use the Biot-Savart's law to find a finite value of force exerted by q1 on q2. The angle theta according to them is the angle between the direction of velocity of q1 to radius vector, in this case 90.

Then they find the force exerted by q2 on q1. The angle comes out to be 180, the sine of which is 0. Thus the force comes out to be 0. Thus they conclude that Newton's law that "Every action has an equal and opposite reaction" has been proved false, as q1 exerts force on q2 but q2 doesn't exert force on q1.

My views are, they way they're taking the angles may be wrong. But I was unable to find a proper reference to it, and I'm still scouring through websites to get more details.

Secondly, their conclusion seems to be a little fishy. This doubt has been spinning my mind, and I though of asking it here, so that this doubt can be cleared.

Thanks,
Sleek.

Last edited by a moderator: May 3, 2017
2. Aug 1, 2007

### chaoseverlasting

The force on q1 by q2 is the opposite (multiply by -1) of the force by q2 on q1. The way they have taken the angles is wrong. This obviously follows from newton's third law.