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let one charge is moving and another charge is stationary (compulsory). Then the electric force between them can be calculated by coulomb's law?

Qmechanic
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KHJ
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1 Answers1

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Yes. In the frame of the stationary charge $Q$, the electric field is: $$\mathbf E_Q = \frac{kQ\mathbf r}{r^3}$$ The force at a (moving) test charge $q$ is $\mathbf F = q\mathbf E$.

But the inverse is not true. The force from the test charge in $Q$ is not equal and opposite. In the frame of $Q$, the electric field of a moving charge is not simply: $$\mathbf E_q = \frac{kq\mathbf r}{r^3}$$ And there is also a magnetic field due to its movement in relation to $Q$ frame.

Claudio Saspinski
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  • Thank you for your good answer – KHJ Nov 04 '23 at 21:05
  • The force from the test charge in Q is not equal and opposite. Why? Have you calculated it? Do you think that the total momentum of the two charges is changing? – Ghoster Nov 05 '23 at 00:25
  • @Ghoster, Do you agree with this answer? or not? – KHJ Nov 05 '23 at 07:03
  • @Ghoster the momentum conservation on movement of charges includes emission of EM radiation. Looking only at the charges, the Newton's third law doesn't apply. – Claudio Saspinski Nov 05 '23 at 12:47
  • The OP was vague regarding the motion. If the moving charge is in uniform motion, there is no radiation and the forces are equal and opposite. So I think your answer is misleading. – Ghoster Nov 05 '23 at 17:18