My idea is to make a gun-like model which would be the source of a changing magnetic field so that Eddy currents are produced in the bullet. Would it be enough to stop a moving bullet? I'm posting a rough picture of my idea. I just have to get the value of EMF of the source and the bullet should theoretically stop inside the solenoid, shouldn't it?
Also, if there's a way to create a magnetic field outside the "gun", so as to stop the bullet mid air, please enlighten me with the method.
You can certainly slow it down - the principle is very nicely shown here and used in practice for braking.
To figure out what you'd actually need to render it harmless, you need to do some calculations. Most calculations are done for disk brakes(see this answer), but we can do dimensional analysis to arrive at a very crude estimate. The braking force will be proportional to square of the magnetic field linearly proportional to velocity and inversely proportional to resistivity (a better conductor is better). It's also proportional to something with units of volume. For disk geometry, in the form of area times thickness, but here we don't have two easily separable directions, and the currents and field don't necessarily penetrate through the entire bulk, so the actual force will be smaller.
$$F\sim vB^2 V/\zeta$$ Deceleration in this approximation doesn't depend on the shape and volume (which will cause the actual deceleration to be slower):
$$a=\frac{F}{\rho V}\sim vB^2/(\zeta \rho)$$ This can be written as $$\dot{v}=-v/\tau\Rightarrow v=v_0 e^{-t/\tau}$$ where $\tau=\zeta\rho/B^2$ is the characteristic stopping time. A stopping distance is then $x_0=v_0\tau$. you need a magnetic field: $$B=\sqrt{\zeta\rho v_0/x_0}$$
For a lead bullet, $\zeta=22\cdot 10^{-8}\,\rm\Omega m$, $\rho=11.3\cdot 10^3\,\rm kg/m^3$. To stop a bullet in $x_0=1\,\rm m$ long distance, starting at typical velocity $v_0=300\,\rm m/s$, you need $B=0.9\,\rm T$. A large, but still reasonable field, but not entirely crazy - it can be done.
The answer is "yes", but you are going to need a monstrously powerful field if you want to stop it over a short distance. A typical rifle bullet has 2 kJ of energy and that has to be turned to heat. It acquired that energy over a distance of around 40cm typically using quite an efficient system
However, there is a variation of your idea being developed to defeat the jet of liquid metal created by HEAT rounds impacting armor. It uses a spaced conducting armour connected to a powerful capacitor bank. When the liquid metal (usually copper) bridges the plates it discharges the capacitor through the jet and the resulting magnetic field disrupts its profile leading to reduced penetration.
Another bit of fun that is experimentally relevant - Mythbusters! At 3:30 they fire a bullet across the faces of 10 large Neodymium magnets. Typically the field intensity at the surface of such a magnet would be about 1T, however, it's not clear how close to the surface the bullet traveled. Nevertheless, there was a deflection and the bullet did appear to decelerate and tumble.
I'll risk objecting, and saying the answer is: "No, of course not". At least two very compelling reasons exist why the answer must be "no" (plus some minor considerations).
First, assume that a bullet moves at, say, 500 m/s and has a kinetic energy of 1kJ (that's about what some .357 cartridges will deliver, a hunting rifle will have 2-3 times as much, and .50BMG would have 16 times as much). Also, assume that your eddie bullet-stopper is half a meter long. It cannot be much longer or it will be impractical.
The generated field will somewhat extend beyond the device's length of course, but this is rather inconsequential (inverse-square law). To compensate for that, assume the device operates at 100% efficiency (which is most certainly not the case).
Given the bullet's speed and the distance within which it must stop, you have 1/1000 second during which 1kJ of kinetic energy needs to be "countered" one way or another (irrespective of how the device works, someone or something must somehow absorb or counter the kinetic energy).
That means that your device must have an effective output of at least 1MW.
The idea of carrying around a device with a megawatt output (...plus suitable power source!) is just ridiculous. Even assuming you have a suitably small power source, if you want to use cables that are approximately the thickness of the stubborn things that one plugs onto a car battery, you would have to cramp up the voltage to 10,000V in order to keep the current within the low hundreds of amperes. Not much thrilled with the idea of carrying such a thing around.
Installing a megawatt device on anything that isn't the size of a warship -- or at least an airplane -- isn't reasonable.
Which brings us to point #2: If it is possible to decelerate something (a bullet, if you will) with a given method, it should also possible to accelerate it with a similar, related approach. Basically, one could consider the opposite of an eddie brake a coil gun (or rail gun, if there is a slide involved), even if they are only vaguely related and don't operate on exactly the same principle.
U.S. military has been spending billions and decades on the development of such devices, and the only working implementations (well, kind-of working) are installed on... you guessed it: aircraft carriers.
Those are admittedly high-velocity guns not quite comparable with a "normal" bullet, but a man-carryable coil gun shooting subsonic bullets would surely be something that the military would like to have as well. No sound, no muzzle flash, perfect for snipers. You can be certain they tried. I'm not aware any such thing exists (no, Schwarzenegger movies don't count).
That implies that your chances of successfully designing and building anything that's in any way related are zero. If this was possible, it would have been done long ago.
As a minor consideration, an eddie apparatus that has a power output in the megawatt range would have very non-trivial interactions with your body, possibly just as bad as the ones caused by a bullet. Parts of your body contain non-trivial amounts of material that will interact strongly with magnetic fields (all parts do, but all are not equal). This is what one uses when doing a MRT image from your body (but with a duration of approx. 400-800ms rather than 1ms, and consequently much weaker field). Specific absorption rate typically goes up as the pulse duration goes down too, so... expect to be warmed up somewhat.
The possible neurological effects of a strong pulse are hard to predict, but it is not unreasonable to expect some. During research of MRT effects on living beings, nerve conduction velocity in rats has been shown to increase after having exposed to moderately strong magnetic fields (0.2T), for example. Very likely, the observable effects are still one or two orders of magnitude too weak to cause something drastic like e.g. cardiac arrythmia, but I wouldn't want to bet my life on it.
So even if this apparatus could be made to "work" from a technical point of view (i.e. "work" insofar as stopping the bullet), it might very possibly still be of no practical use.
