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Chhhiral
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Why a generic vector field produces repulsive forces between charges of the same sign? And where can I find a book or a paper in which it is shown?
Thanks, but your answer is equivalent to: take like charges and calculate the Coulomb force. My question is more generalVanadium 50 said:Calculate e-e- scattering and e+e- scattering and take the non relativistic limit. It's probably in every book.
His answer is very appropriate for an "advanced" level response, which is what you asked for by marking the thread as "A". I will adjust the level of the question to more appropriately reflect what you are looking for.Chhhiral said:Thanks, but your answer is equivalent to: take like charges and calculate the Coulomb force. My question is more general
in many books of general relativity I found the statement: a vector field produces repulsive forces between like charges so can not be used to describe gravity ...DaleSpam said:A generic vector field does not produce repulsive forces between like charges. A Coulomb field does. The reason why is simply the way the Coulomb field is defined:
https://en.m.wikipedia.org/wiki/Coulomb's_law#Vector_form
I have never seen such a statement. Can you provide the reference.Chhhiral said:in many books of general relativity I found the statement
Gasperini, Maurizio. Relatività Generale e Teoria della Gravitazione. Springer Milan, 2015. pag:27DaleSpam said:I have never seen such a statement. Can you provide the reference.
I'm trying to understand why a vector field can not be used to describe gravity. Not because the force of Coulumb is so defined or because the Lagrangian of the electromagnetic field leads to Bhabha scattering...DaleSpam said:His answer is very appropriate for an "advanced" level response, which is what you asked for by marking the thread as "A". I will adjust the level of the question to more appropriately reflect what you are looking for.
Hobson, Michael Paul, George P. Efstathiou, and Anthony N. Lasenby.General relativity: an introduction for physicists. Cambridge University Press, 2006. pag:191DaleSpam said:I have never seen such a statement. Can you provide the reference.
You have been so quick to downgrade my question ... but now you do not answer ... maybe do you want other references? Please answer me, is a very important question for me... thanksDaleSpam said:His answer is very appropriate for an "advanced" level response, which is what you asked for by marking the thread as "A". I will adjust the level of the question to more appropriately reflect what you are looking for.
A vector field is a mathematical concept used to visualize and represent the direction and magnitude of a vector quantity at every point in a given space. It is usually represented by arrows, with the length and direction of the arrows indicating the strength and direction of the vector at that point.
A scalar field is a mathematical concept that assigns a scalar value (a numerical value) to every point in a given space. In contrast, a vector field assigns a vector (with both magnitude and direction) to every point in the space. This means that a vector field contains more information than a scalar field.
Vector fields have a wide range of applications in various fields such as physics, engineering, and fluid mechanics. They are used to represent fluid flow, magnetic fields, electric fields, and other physical phenomena. They are also used in computer graphics to generate realistic simulations of natural phenomena.
Vector fields are typically visualized using arrows, as mentioned earlier. These arrows can be 2D or 3D depending on the dimensionality of the space. Color can also be used to represent the magnitude or direction of the vectors. Other visualization techniques include streamlines, which show the paths of particles moving through the vector field.
Vector fields are used in data analysis to analyze and interpret large datasets. They can help identify patterns and trends in the data and can also be used for predictive modeling. In addition, vector fields are often used in machine learning algorithms to represent and analyze complex data sets.