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I know what i am asking is not possible , but the scenario what i am pondering over I cannot explain. So let's assume their is a huge magnet subtending from the top of the burj khalifa (Tallest building, Dubai). The magnet is so powerful it can pull objects from the ground below. I keep a series of metallic balls which get raised to the height where the magnet is thus gaining potential energy. Where does this energy come from? I mean this Question can be a totally stupid one. but i can't think of an explanation

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The energy comes from the magnetic field's potential energy. When the balls are attracted to the magnet, some of the potential energy of the magnet field gets converted into the kinetic energy of the balls and the gravitation potential energy of the balls.

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The magnetic field stores energy by existing. When the ball goes from being far from the magnet to close to it the field produced by the ball + magnet will store less energy because the field will be slightly less intense, overall. So, as Noah P said, the work was done when the strong magnet was created.

It's the same question, fundamentally, as if I lifted a rock to the top of the tower and dropped it, where was it stored while I waited to drop it? Answer: in the slightly more intense gravitational field generated between the ball and Earth when they're farther apart than when they're close.

In SI units, the energy density stored in an electromagnetic field is: $$u_{EM} = \frac{1}{2} \mathbf{E} \cdot \mathbf{D} + \frac{1}{2} \mathbf{B} \cdot \mathbf{H},$$ where $\mathbf{E}$ is the electric field strength, $\mathbf{D}$ is called the displacement field, both $\mathbf{B}$ and $\mathbf{H}$ are known as magnetic fields, though they have different units. For more, look up information on the Maxwell stress tensor.

A similar equation holds for the pre-Einstein gravitational field. The energy density stored in a gravitational field is: $$u_G = \frac{1}{8\pi G} \mathbf{g}^2. $$

In either case, the total energy stored in the field is the integral over the volume the fields are in.

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A constant magnetic field doesn't do any work on a moving charge. This, however, doesn't mean that a magnetic field can't do work if it is not constant. The field has an energy density of B^2 / 2u

and this energy can be converted into work if the field changes, e.g. by introducing a magnetic material. It's the change in the field strength when the magnetic material is being introduced that allows for such a system to perform mechanical work. In case of electromagnets the necessary energy comes from the electric current that powers the magnet.

In a quasi-static configuration, i.e. when the magnetic fields change slowly, we can calculate the total energy of the system (i.e. the energy in the fields as well as the energy in the magnetized materials) as a function of the position of the magnetic materials. For linear magnetic materials we can use B = μH

and then the total energy of the system becomes

E magnetic = ∫ HB dV

The system will be most stable in the configuration in which this total energy is the smallest, i.e. we can treat this almost like a potential problem. I say almost because we are usually dealing with extended magnetized bodies, i.e. we need to consider both the position and the orientation of the bodies, so it is a little more complicated than in the case of a gravitational or electric potential.

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Does a magnet create energy?

No. The books always balance.

...The magnet is so powerful it can pull objects from the ground below. I keep a series of metallic balls which get raised to the height where the magnet is thus gaining potential energy. Where does this energy come from?

The metallic balls. To understand this, imagine you're standing at the top of 2,722ft tower with a 1kg metal ball in your hand. You drop it. It plummets to Earth, and smashes into a car. KABOOM! The car is smashed up because the ball hit it with considerable kinetic energy. Where did this kinetic energy come from? It didn't come from the Earth, or from the Earth's gravitational field. It came from the ball. When you dropped it, gravity converted gravitational potential energy in the ball into kinetic energy. After the kinetic energy was dissipated the ball was left with a mass deficit.

Note that if you have two equal-sized gravitating bodies which fall towards each other, the kinetic energy and mass deficit is shared equally. But if one body is much larger than the other, this is not true. Momentum p=mv is shared equally, but kinetic energy KE=½mv² is not. When one body is so much more massive than the other that you cannot detect it moving towards the common centre, you discount its motion and say the smaller body has all the kinetic energy.

Also note that you have to do work on your ball to lift it up to an altitude of 2,722ft. Let's say you throw it up straight up into the air. You give it considerable kinetic energy whilst giving the Earth effectively none. Gravity then converts this kinetic energy into potential energy. This is not in the Earth, or the Earth's gravitational field, it's in the ball. Nowhere else. You can work this out because if you threw the ball upwards at 11.7km/s it would have escape velocity. It would leave the Earth forever, taking all it kinetic/potential energy with it. Because the work you did on the ball and the energy you gave to the ball increases the mass of the ball. It's the inverse of the mass deficit. This is why potential energy is mass-energy.

OK, now lets replace the Earth with a magnet. Your ball starts off stuck to the magnet, and you have to do work on it to pull it away from the magnet. When you let it go it "falls" towards the magnet. Potential energy is converted into kinetic energy which then gets dissipated, and the ball is left with a mass deficit. It's similar for the electron and the proton. There's a mass deficit of 13.6eV, and most of this can be assigned to the electron, because it's 1837 times less massive than the proton. A combination of two systems is fairly straightforward. If you're on the ground and your ball falls up towards the magnet, less potential energy is being converted into kinetic energy. If the Earth wasn't present, there would be more conversion into kinetic energy, and the ball would hit the magnet at a higher speed. The books always balance.

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  • $\begingroup$ Would the downvoter care to comment? And point out any errors in the above? $\endgroup$ – John Duffield Sep 8 '16 at 15:54

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