Magnetic Field Due To Moving Charges: An Unsound Conclusion?

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SUMMARY

The discussion centers on the application of the Biot-Savart Law to analyze the magnetic field generated by two moving charges, q1 and q2, with respective velocities v1 and v2. The conclusion drawn by a participant, claiming that Newton's third law is violated because the force exerted by q1 on q2 is not reciprocated, is fundamentally flawed. The error lies in the misinterpretation of the angles used in the calculations, particularly in the application of the sine function in the force equations. The correct understanding confirms that the forces are indeed equal and opposite, adhering to Newton's third law.

PREREQUISITES
  • Understanding of Biot-Savart Law for magnetic field calculations
  • Familiarity with Newton's laws of motion, particularly the third law
  • Basic knowledge of vector mathematics and trigonometry
  • Concepts of electric charge and motion in electromagnetic fields
NEXT STEPS
  • Study the Biot-Savart Law in detail, focusing on its applications in electromagnetism
  • Review vector mathematics, particularly the cross product and its geometric interpretations
  • Explore case studies demonstrating Newton's third law in electromagnetic contexts
  • Investigate common misconceptions in physics related to forces and motion
USEFUL FOR

Students of physics, educators teaching electromagnetism, and anyone interested in the principles of force interactions in moving charge systems.

Sleek
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Homework Statement


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.

http://img524.imageshack.us/img524/701/radiusju7.th.jpg

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.

Homework Equations



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

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:
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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.
 

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