When I failed to get answers for the red light curved bands of the Alien spaceship that had flown over Kampala, and aurora represent another enigma, and strong force is only a theoretical elusion, that neutron is too hard to replicate, and Quantum Mechanics became another land. I returned back into history searching for a clue, it all concentrated in the history of the magnetic field and the following equations shows that.
When the magnetic effects due to electric current was discovered in 1819 by Hans Christian Oersted [1], André Ampère determined the circular shape of the magnetic field around conductor carrying electric current [2], and gave formula for a force between two conductors carrying electric current as:
Where, k is 10 N/A, I and I are the current in both conductors in amperes, l is length of the conductors in meters, d is distance between both conductors in meters and the force F is in Newton.
On the other hand, magnitude of magnetic field around moving electrons or protons or their circular magnetic field (CMF) [3, 4, 5] is given by
Where, c is the speed of light, q is the particle's charge in coulombs, v is the charged particles velocity in ms-1, rm is the magnetic radius at which the CMF is measured (representing rme and rmp or electron's and proton's magnetic radius respectively). The circular magnetic field B2 is given in Tesla.
The Lorentz force is given with electric-magnetic parameters by
Where, is the angle between the trajectory and the fields the force Fe.m. is in Newtons.
Equations (1 and 3), while expressing magnetic forces; they were formulated using electrical parameters.
Mechanism behind the attractive and repulsive forces given by Eq.(1) is due to the interaction of magnetic lines of force attractively or repulsively, therefore, the force is expressed magnetically by
Where, constant k= 2x10-7 Newton per square ampere, Bc1 and BC2 are circular magnetic field (CMF) around both conductors (in Tesla) produced by conductors C1 and C2 respectively, while r1 and r2 are the CMF's radii in metre, l1 is the length of the conductor in metres.
For the force given by Eq.(3), relating it to Eq.(2), therefore the magnetic force resulted from the Magnetic Interaction, is given by
Where, is the angle between the two fields, B1 is the magnetic field in Tesla, B2 is the CMF produced electrons and protons given by Eq. (2) in Tesla, rm is the CMF's radius in meters and the magnetic force F is in Newtons.
And read more from the following papers: