# Showing tangential magnetic force by experiment

Theoretical explanation of tangential magnetic force and the experiment of rotating coil. Tangential magnetic force is tangent to the current on which it acts. For the classical theory this force does not exist. However, my experiment « Continuous rotation of a circular coil experiment » showed that a force tangent to the current must be there. If tangential magnetic force exists, why was it not detected in almost 200 years?

Showing tangential magnetic force by experiment
PDF http://pengkuanem.blogspot.com/2018/05/showing-tangential-magnetic-force-by.html
or

# Plasma under Coulomb magnetic force

Nuclear fusion reactors use strong magnetic field to confine plasma in reaction chambers. The magnetic field is so designed that plasma should follow field lines which do not encounter the chambers’ wall. But it seems that a mysterious force pushes plasma off its track. For explaining this force, Coulomb magnetic force law for plasma is derived.

Plasma under Coulomb magnetic force
PDF http://pengkuanem.blogspot.com/2018/04/plasma-under-coulomb-magnetic-force.html
or

# Coulomb magnetic force

The relativistic length contraction effect and changing distance effect produce 2 different magnetic forces. Together they form complete magnetic force.
I have derived 2 magnetic forces with Coulomb’s law and charges’ velocity. The first force dFlc is derived in «Length-contraction magnetic-force between arbitrary currents». The second force dFcd is derived in «Changing distance effect». dFlc and dFcd are added together to give the expression for complete magnetic force dFcm.

Coulomb magnetic force
PDF http://pengkuanem.blogspot.com/2018/03/coulomb-magnetic-force.html
or

PDF Changing distance effect http://pengkuanem.blogspot.com/2018/03/changing-distance-effect.html or

# Continuous rotation of a circular coil experiment

There is a long standing debate about whether tangential magnetic force exists. In «Tangential magnetic force experiment with circular coil» I discussed this force and presented an experiment that showed the action of this force. But, as the rotation of the coil in that experiment was limited to a small angle, it does not show that tangential force exists all over the coil. So, I have carried out the present experiment that shows continuous rotation of the coil to make clear that tangential force has the same value around the coil

PDF Continuous rotation of a circular coil experiment http://pengkuanem.blogspot.com/2017/06/continuous-rotation-of-circular-coil.html

# Tangential magnetic force experiment with circular coil

If magnetic force is to respect Newton’s third law, there should be a recoil force on the vertical current which is Ft. This force is tangent to the current I1 and called tangential magnetic force. Some physicists claim that tangential magnetic force exists, this claim is supported by some experiments such as the rail gun recoil force shown by Peter Graneau and Ampère’s hairpin experiment, see Lars Johansson’s paper. But these experiments did not convince the main stream physicists and tangential magnetic force is rejected. I have carried out an experiment to show tangential magnetic force acting on a circular coil.

PDF Tangential magnetic force experiment with circular coil http://pengkuanem.blogspot.com/2017/06/tangential-magnetic-force-experiment.html

# Length-contraction-magnetic-force between arbitrary currents

In ≪Relativistic length contraction and magnetic force≫ I have explained the mechanism of creation of magnetic force from Coulomb force and relativistic length contraction. For facilitating the understanding of this mechanism I used parallel current elements because the lengths are contracted in the direction of the currents. But real currents are rarely parallel, for example, dIa and dIb of the two circuits in Figure 1. For correctly applying length contraction on currents in any direction, we will consider conductor wires in their volume and apply length contraction on volume elements of the wires.

PDF Length-contraction-magnetic-force between arbitrary currents http://pengkuanem.blogspot.com/2017/05/length-contraction-magnetic-force.html

# Relativistic length contraction and magnetic force

Magnetism is intimately related to special relativity. Maxwell’s equations are invariant under a Lorentz transformation; the electromagnetic wave equation gives the speed of light c. Many have explained magnetic force as a consequence of relativistic length contraction, for example Richard Feynman in page 13-8 of his ≪The Feynman Lectures on Physics, Volume II≫ and Steve Adams in page 266 in his ≪Relativity: An Introduction to Spacetime Physic≫. If magnetic force is really created by relativistic length contraction, we should be able to derive the expression for magnetic force from the length contraction formula. And indeed we can, as I will show below.

PDF Relativistic length contraction and magnetic force http://pengkuanem.blogspot.com/2017/04/relativistic-length-contraction-and.html

# Lists of binary sequences and uncountability

Creation of binary lists, discussion about the power set of ℕ, the diagonal argument, Cantor’s first proof and uncountability. Binary system is kind of magic because it can express natural numbers, real numbers and subsets of natural numbers. Below, we will create lists of binary sequences to study the uncountability of the power set of ℕ and real numbers.

1.Infinite list of binary sequences
2.About the Power set of ℕ
3.Frame of Natural Infinity
4.List of numbers smaller than 1
a.Creation of the numbers
b.Denseness of R..
c.Completeness of R..
d.Real numbers in [0,1[
7.Conclusion

PDF Lists of binary sequences and uncountability
http://pengkuanonmaths.blogspot.com/2016/11/lists-of-binary-sequences-and.html

# Continuity and uncountability

Discussion about continuity of line, how continuity is related to uncountability and the continuum hypothesis.
The real line is made of real numbers which are points. Points are discrete objects, but lines are continuous objects. How does continuity arise out of discreteness when points make line? The idea of uncountability solves this problem. Rational numbers are countable, the line they make contains holes. Real numbers are uncountable, the line they make is continuous. So, continuity must be created by the uncountability of the points of a continuous line. One can imagine that uncountable points are so numerous on the real line that real numbers are squeezed together.

Georg Cantor called the set of real numbers continuum, so he probably thought of creating continuity with discreteness when inventing uncountability. But, what does continuity really mean?

PDF Continuity and uncountability
http://pengkuanonmaths.blogspot.com/2016/09/continuity-and-uncountability.html