The opposit point charge of same magnitude separated by distance 2d electric potential mid way between them is
Answers
Answer:
Really the potential is indeterminate as this could be a floating system placed somewhere in a space potential field which you did not state.
Also it is not enough to tell me that the point P is mid way between two opposite charges and they have a +q and a -q charge on them . You see, the structure on which the charges are mounted could be different in shape and the charges would place themselves according to the shape of the structure and so the field equipotential lines in field plotting, is not as simple as one thinks. Fields are the not only due to charges but also due to shapes and so again this question has indeterminate answer. Anyone doubting this would be welcome to assume one charge is placed on a spherical metallic terminal with a constant rate of change on its surface while the other opposite charge is places on a square metallic terminal with sharp corners........ anyone doing this and plots the resulting field would have the surprise of his life and they who made a calculation should go and consider the ideology they assumed.
But to give an answer to the question, using pure SYMMETRY alone, then the field plotting of the system with respect to itself, assuming there is nothing around it to disturb the electric fields set up by the symmetrical shape and the charges, , the symmetry alone, whatever be the shape of the terminals on which +q and -q are deposited, then there will be one equipotential line formed as a straight line through the "centre" acting as a mirror, where one charge would be mirrored of the other, This would mean that this equipotential straight line at the mid way point has a ZERO voltage as the charges are equal and opposite and the structure is perfectly SYMMETRICAL and nothing exists around it.
There are no conventional formulas that can handle that but it needs to be a good software which could also handle Navier Stokes equations for a source and a sink. Hope that puts some more light on the subject.
You know the other day I was trying to invent an electro- mechanical model which represents the electron with its charge, This model of mine needs to solve all the behaviour of the charged electron irrespective where it is placed as
1. A stationary isolated electron with its negative charge, surrounded by nothing.
2. A free isolated electron placed in an electric field with or without an rate of change with time.
3. A free stationary isolated electron placed in a Magnetic field with or without a rate of change with time or distance.
4. A fast moving electron going past a Magnetic field with or without a rate of change with time or distance.
5. A free isolated electron placed in an electric and a magnetic field at the same time.
The electron model I came up, in order to react to all the situations and states described above, MUST include in it A MASS, A CHARGE, AN ELECTRIC FIELD , AND A MAGNETIC FIELD. I arranged for the whole electron charge to be divided into small charges each individual charge on the front point of a short arrow whose shaft represents the direction of an electric field and a curling magnetic field around the shaft replacing the feathered end of the arrow. A stationary electron would have all its arrows pointing in different directions and so the elemental masses and electric charges would be cumulative and this would make its presence in the outside world , while the curling magnetic fields would be destructive and it would not be felt in the outside world.
Now if the stationary electron was given either a velocity, or placed in an electric or a magnetic field with a rate of change' then not only the elemental mass and electric charge would be cumulative but the curling magnetic fields will line up as the arrows will line up and the elemental curling magnetic fields will become cumulative and the moving electron will make its magnetic field conspicuous to the outside world.
So when answering this question, I could not smile a little at my own ambitions and with my electro-mechanical model of an electron and its mass, electric negative charge, its electric and magnetic contents making themselves conspicuous or not to the outside world, depending on the external states they are in. Well the field plotting picture of what was termed above and assumed to be a symmetrical arrangement, this would have in it, within the electric charges +q and-q , on the metal plates, a wonderful array of magnetic fields which exist but in this case are destructive in their nature. This work is making me sweat, but the model I am putting together is just beautiful and so elegant and believe me, I need to go to sleep.
Explanation:
Answer:
Really the potential is indeterminate as this could be a floating system placed somewhere in a space potential field which you did not state.
Also it is not enough to tell me that the point P is mid way between two opposite charges and they have a +q and a -q charge on them . You see, the structure on which the charges are mounted could be different in shape and the charges would place themselves according to the shape of the structure and so the field equipotential lines in field plotting, is not as simple as one thinks. Fields are the not only due to charges but also due to shapes and so again this question has indeterminate answer. Anyone doubting this would be welcome to assume one charge is placed on a spherical metallic terminal with a constant rate of change on its surface while the other opposite charge is places on a square metallic terminal with sharp corners........ anyone doing this and plots the resulting field would have the surprise of his life and they who made a calculation should go and consider the ideology they assumed.
But to give an answer to the question, using pure SYMMETRY alone, then the field plotting of the system with respect to itself, assuming there is nothing around it to disturb the electric fields set up by the symmetrical shape and the charges, , the symmetry alone, whatever be the shape of the terminals on which +q and -q are deposited, then there will be one equipotential line formed as a straight line through the "centre" acting as a mirror, where one charge would be mirrored of the other, This would mean that this equipotential straight line at the mid way point has a ZERO voltage as the charges are equal and opposite and the structure is perfectly SYMMETRICAL and nothing exists around it.
There are no conventional formulas that can handle that but it needs to be a good software which could also handle Navier Stokes equations for a source and a sink. Hope that puts some more light on the subject.
You know the other day I was trying to invent an electro- mechanical model which represents the electron with its charge, This model of mine needs to solve all the behaviour of the charged electron irrespective where it is placed as
1. A stationary isolated electron with its negative charge, surrounded by nothing.
2. A free isolated electron placed in an electric field with or without an rate of change with time.
3. A free stationary isolated electron placed in a Magnetic field with or without a rate of change with time or distance.
4. A fast moving electron going past a Magnetic field with or without a rate of change with time or distance.
5. A free isolated electron placed in an electric and a magnetic field at the same time.
The electron model I came up, in order to react to all the situations and states described above, MUST include in it A MASS, A CHARGE, AN ELECTRIC FIELD , AND A MAGNETIC FIELD. I arranged for the whole electron charge to be divided into small charges each individual charge on the front point of a short arrow whose shaft represents the direction of an electric field and a curling magnetic field around the shaft replacing the feathered end of the arrow. A stationary electron would have all its arrows pointing in different directions and so the elemental masses and electric charges would be cumulative and this would make its presence in the outside world , while the curling magnetic fields would be destructive and it would not be felt in the outside world.
Now if the stationary electron was given either a velocity, or placed in an electric or a magnetic field with a rate of change' then not only the elemental mass and electric charge would be cumulative but the curling magnetic fields will line up as the arrows will line up and the elemental curling magnetic fields will become cumulative and the moving electron will make its magnetic field conspicuous to the outside world.
So when answering this question, I could not smile a little at my own ambitions and with my electro-mechanical model of an electron and its mass, electric negative charge, its electric and magnetic contents making themselves conspicuous or not to the outside world, depending on the external states they are in. Well the field plotting picture of what was termed above and assumed to be a symmetrical arrangement, this would have in it, within the electric charges +q and-q , on the metal plates, a wonderful array of magnetic fields which exist but in this case are destructive in their nature. This work is making me sweat, but the model I am putting together is just beautiful and so elegant and believe me, I need to go to sleep .
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