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Two conducting solid sphere,one with charge Q1 and radius R1 and the other with charge Q2 and radius R2 are kept far away

$$Q_1=5Q_2 \text{ and } R_1=5R_2 $$

If these spheres are connected with conducting wire, then the potential is same at the two ends of the wire.

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I saw these questions in a pdf of a textbook, i am unable to answer these, good explanations would be appreciated...these questions are as follows----

1. Is the potential at a point between the two ends of the wire the same as potential at the end? In other words, is the potential same throughout the wire? if yes, why??

Remember, potential from a sphere depends upon "x" displacement from the centre by KQ/R.

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  • $\begingroup$ @ThePhoton it wasn't an assumption, you can actually calculate Potential at the two points and it would came out to be same as spheres are placed far away( it signifies that the potential at any end is only due to the sphere it is connected to , you can neglect effect of other sphere) $\endgroup$
    – TonyPhysicslover
    Apr 30 at 15:35
  • $\begingroup$ @ThePhoton and please use numbers to indicate which part of the question you are answering $\endgroup$
    – TonyPhysicslover
    Apr 30 at 15:36
  • $\begingroup$ @ThePhoton, in my question,charges are already of same kind in the sphere , and both sphere have same potential at the surfaces already so no current would be generated $\endgroup$
    – TonyPhysicslover
    Apr 30 at 17:17
  • $\begingroup$ @ThePhoton What I really want to know are the answers of the three questions that I have listed $\endgroup$
    – TonyPhysicslover
    Apr 30 at 17:18

1 Answer 1

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Assuming the the sphere separation is large enough that the surface charge densities remain spherical, and assuming that charges from the wire do not significantly change that distribution, then electrons in the wire will be attracted toward the “near-by” sphere, leaving a positive charge in the wire with its maximum at the “null” point (where the fields from the two spheres are equal). The resulting charge distribution in the wire will give a resultant zero electric field in the wire connecting the two spheres which are at the (unchanged) same potential.

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  • $\begingroup$ +1, I understood your point that they would get attracted only if the charges are positive, but i didn't clearly got the point of null point.Also, can you illustrate more how the charge distribution would be ? $\endgroup$
    – TonyPhysicslover
    Apr 30 at 18:57
  • $\begingroup$ I also want to know what would have happened if charges are negative . $\endgroup$
    – TonyPhysicslover
    Apr 30 at 18:57
  • $\begingroup$ If the spheres are negative, electrons in the wire will be repelled by the nearest sphere putting the maximum density at the null point, and leaving E = 0 in the wire $\endgroup$
    – R.W. Bird
    May 1 at 13:36
  • $\begingroup$ Why electron does not flow through nearby spheres and only got attracted ? What is preventing them ? $\endgroup$
    – TonyPhysicslover
    May 4 at 13:47
  • $\begingroup$ My assumption is that the quantity of charge moving to or from a thin wire is insignificant as compared with the charge on each of the spheres. I can only suggest that the charge distribution in the wire would have to be what is required to give a resultant E field of zero. $\endgroup$
    – R.W. Bird
    May 4 at 15:59

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