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- Mathematical and Physical queries in regards to Electromagnetic Fields and their manipulation of Space-Time.

**Summary:**Mathematical and Physical queries in regards to Electromagnetic Fields and their manipulation of Space-Time.

I recently started looking into Einstein's Field Equations, to get a better understanding of how mass distorts and curves the plane of Space-Time, however from doing this I understood that it isn't actually mass that distorts Space-Time but Energy - which is directly proportional to the mass of an object (E=mc²).

So from this, Energy creates the sensation of Gravity, rather than the mass of an Object.

This made me think that if a large enough magnetic field was generated, that the Energy held within the magnetic field could produce a Gravitational effect - so I tried doing the calculations to see what figures we would be looking at in regards to this...

We know that the Earth's Gravitation Acceleration is about 9.81 m/s²

This is calculated from:

a = mG / d²

Where a is Gravitational Acceleration in m/s²; m is the mass in Kg; G is the Gravitational Constant of 6.67408x10

^{-11}; and d is the distance from the object.

We can re-arrange this to solve for m:

m = ad² / G

Because we know mass is directly proportional with Energy from E=mc², we can substitute this into the equation above:

E = (ad² / G)c² ∴ E = ac²d² / G

Solving for 'a' we get:

a = EG / c²d²

If we were to make a coil to generate the Magnetic field we needed, then we can use the below equation to find the Induced Energy (E) from the Inductance (L) and the Current (I) on the coil:

E = 1/2 LI²

If we substituted the above formula for E in our previous formula, then we get this:

a = GLI² / 2c²d²

If we were to make the coil, we would need to calculate the amount of Inductance generated; using this equation we can do that:

L = N²∙μ

_{0}∙μ

_{r}∙(D/2) ∙ (ln(8D/d)-2)

Where N is the number of turns in the coil; μ

_{0}is the Permeability of free space; μ

_{r}is the Relative Permeability of the Core; D is the diameter of each coil; and 'd' is the diameter of the cable used. I got this formula here

If we were to use a 99.85% pure Iron core, with a Relative Permeability of 200,000; each coil being 0.2m in diameter with 50mm² cable for 400A of current; and assuming that we would be standing 1m away from it - then we can start putting this equation together.

Unfortunately this is where it gets ridiculous - using all of the above, to get a meaningful Gravitation Acceleration; N has to be an obscenely large number... in this case 600,000,000,000 coils...

L = 600,000,000,000²∙1.26x10

^{-6}∙200,000∙(0.2/2) ∙ (ln(8∙0.2/(2∙√(50/π))-2) = 2.98664x10

^{22}H

a = 6.67408x10

^{-11}∙2.98664x10

^{22}∙400² / 2∙299792458²∙1²

a = 1.77m/s²

This is slightly more than the gravitational pull of the moon - 1.62m/s²

Now...

This is the mathematical side of it, practically speaking that would never work for multiple reasons but perhaps mainly because the vast amount of cable you'd actually need to do this (enough for 50mm² cable to go around the Earth 9.5 million times).

This is why I have come on here to discuss it, so; first of all - is my maths correct?

Second of all, is there any current technology or method that can be used to increase Inductance without having to do 600 billion coils?

Is there a material with a higher Relative Permeability than the 99.85% Pure Iron? I found this 200,000 value after googling it, so not sure if it correct!

My last question, is more ignorant than the others - I have heard that it is possible to get Negative Inductance - I know nothing about it, but the calculations show Gravitational Acceleration going negative when there is Negative Inductance - would this "straighten out" the existing curvature of Space-Time, nulling Gravity?

Thanks!