Wiring LED light strips in car
Your original schematic isn't clear but I think you're trying to use the N-Channel MOSFET as a switch. Since I don't know the current required by your LED strip you should spec one out yourself. This video gives a great introduction to MOSFETs. Below is an explanation for each of the components used.

R1 - current limiting resistor to limit the gate current to reduce voltage oscillations

R2 - pull down resistor to avoid spurious activations by creating a defined voltage level at all times

R3 - load resistor that represents the position of your LED strip in the whole schematic.  







simulate this circuit &ndash; Schematic created using CircuitLab

As others have mentioned, it may be easier to just power the LED strip from a source that's controlled by the ignition. If it's a 12V supply you'll have to use a voltage regulator like the LM7805 to reduce the voltage. It's only rated for about 1A though. If your strip needs more consider a buck converter.