If a charge $q$ is placed at rest at a point $P$ near a wire carrying current $I$, with some distance $x$, it experiences almost no force. However, if the charge $q$ is projected from the point $P$ in the direction of the current, it deflects towards the wire.

Now my question begins. Let us consider this event in front of two observers. One is moving with the velocity $v$ which is also the velocity of the charged body. For the observer who is at rest for him it is a pure magnetic field, and for the moving observer it is an a electric field. However both observers agree with horizontal distance traveled by a charged body as they are unaccelerated with respect to each other. I wonder why can’t the force acting on the charged body effect its vertical velocity.

Please try to understand me this entire process with the help of special relativity. How can’t the vertical velocity of the charged body have no effect.

I am pretty new to this topic. Please correct me, if am wrong completely wrong about this question.

  • $\begingroup$ Can you include a diagram? Which direction are you calling "vertical"? $\endgroup$ – The Photon May 23 at 6:33
  • $\begingroup$ @ThePhoton it is showing “error while uploading the image $\endgroup$ – Sparthunaxx May 23 at 7:01
  • $\begingroup$ @ThePhoton vertical direction is one which the direction of current (I),charged body and the moving observer ,these three are moving along vertical direction $\endgroup$ – Sparthunaxx May 23 at 7:27
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    $\begingroup$ This question is extremely hard to read because the whole first paragraph contains no periods except at the end (making it seem like a single run-on sentence). Additionally the irregular spaces around the commas (sometimes no space, sometimes spaces on both sides, sometimes only on one) don't help either. Please try to use regular formatting and punctuation so that other users have an easier time reading your posts - this will improve your chances at getting an answer considerably. $\endgroup$ – ACuriousMind May 23 at 10:52
  • $\begingroup$ @ACuriousMind Thank you for addressing sir , can you at least understand my question and tell me where am I exactly going wrong. $\endgroup$ – Sparthunaxx May 23 at 18:16

Observer moving with the vertically moving charged object: There is an electric field pointing towards the vertical wire. The electric field has vertical momentum. The charged object gets energy from the electric field. As the electric field has momentum, the charged object gets momentum too. So the charged object accelerates vertically.

Observer not moving with the vertically moving charged object: There is a force pulling the vertically moving charged object towards the vertical wire. As the object gains more energy but not more vertical momentum, its vertical velocity decreases.

This vertical acceleration effect is quite large, as the relevant electric field is large. If the charged object is negative, then the relevant electric field is the field of all the protons in the wire, as that field does the work of pulling the object towards the wire against the large repulsive force between the negative object and all the electrons in the wire.

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