Short circuit protection of mosfet

The name "Short Circuit" comes from an unintentional path for the electrons which is "shorter" than that we intend.

Crudely speaking, the electrons will follow the path of least resistance. Normally we control that flow through our circuit using the components, such as resistors, capacitors, transistors, etc. When an unintentional route between two points is created that is of a lower resistance (thus "shorter") than we want, that is where the electrons will prefer to go. This is what we term a "short circuit".

On an electron level it is no different to any other part of the circuit, but from our point of view it is a bad thing that causes things to happen that we didn't want.

Like many 'output' devices, a coil for producing a magnetic field has a (DC) impedance. This impdance, in combination, with the applied voltage, determines the current, and current and voltage determine the power.

In your case, a 9V DC power and a 0.5 Ohm coil would result in 9/0.5 = 18A current, and 9 * 18 = 162 W power (if your PSU could supply this current, which it can't, as it is rated for 5A). I assume you did not intend to use 162W of power, in which case you have an impedance mismatch: you have a (relatively) high-voltage power, and a (very) low impedance coil. You'll have to change one or the other:

• you could use a lower voltage: assuming a safe 4A, your voltage should be 2V.

• you could increase the impedance of your coil, by using a smaller diameter wire (with more turns, to compensate for the lower current).

• You could use PWM to effectively lower the voltage or increase the impedance (depends on how you look at it), but I would not recommend this: it is much more complex than the transistor-and-relay level electronis that you seem to be more-or-less comfortable with.

PS check Curd's comment, you realy need a base resistor. And you probably need something to absorb the energy in your coil when you switch it off.