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The plan

I'm planning to build and put up a coat hook rack in my flat. My plan is to simply screw 5 hooks into a solid piece of wood and then mount it on the wall. It should look something like this:

only a bit simpler.

However, the wall on which I would like to mount the rack looks like this:

As you can see there are some fuse boxes. The box on the bottom is for the underfloor heating. The boxes above are for fuses. The rack should be mounted above the boxes.

Now to my problem

Due to the fact that I want to mount the rack on a wall with fuse boxes (where there are probably many cables behind the wall), I don't know how (and even if) I can mount a rack onto the wall. I think the use of dowels isn't a good idea because of the cables, correct? I was thinking about mounting it from the ceiling (perhaps using 2 ropes, I know this won't hold just to give you an illustration) but this didn't seem like a good idea to me.

My Question

Do you have any ideas on how to mount the rack onto the wall and do you even think that this would be possible?

Thank you in advance!

In the US code prohibits the panel from being in the vicinity of easily ignitible material with clothes closets specifically listed NEC 240.24.D. So based on that I would say it's not a good idea.

I agree with both isherwood and Ed Beal. You probably shouldn't mount combustibles in front of your electrical panel. That being said if you insist you should be able to comfortably go into the studs an inch without hitting any wires.

Alternative solution

This doesn't always satisfy people's style and this particular image is a pot rack not a wardrobe but you should be able to find some ideas online if you're willing to mount to the ceiling.
This concept may not suit your needs but maybe expand your horizons as to where you have options to put a wardrobe.

If you are concerned about weight I have done pull ups on that pot rack and I weigh 200 pounds.

"Give me my working space back, dangit!"

While your coatrack-over-fusebox proposal may sound like a good idea to an interior designer who doesn't know squat about electrical codes, it's not. In the USA, this would be a quite clear-cut violation of NEC 110.26(B):

(B) Clear Spaces. Working space required by this section shall
not be used for storage. When normally enclosed live parts are
exposed for inspection or servicing, the working space, if in a
passageway or general open space, shall be suitably guarded.

in addition to potentially violating the 110.26(E)(1)(a) requirements for space dedicated to the electrical system and the 110.26(A)(3) requirements for the height of the clear working space around the electrical equipment, depending on how high on the wall the coatrack was placed. This is all atop the issue of having overcurrent devices placed near easily ignitable materials, such as clothing, as is prohibited by NEC 240.24(D):

(D) Not in Vicinity of Easily Ignitible Material. Overcurrent
devices shall not be located in the vicinity of easily ignitible
material, such as in clothes closets.

I put up hooks in my cupboard, which is the equivalent to yours.
I didn't use screws or nails at all, but instead I used a "no nails" adhesive, which is more than strong enough for hanging coats off.

Sometimes the simple solutions are the best.

You're wise to be concerned, but you have some things working in your favor. First, the wiring should be either protected in conduit, or arranged so that it's out of harm's way.

If I was to guess I'd say that there are probably studs on either side of both box locations. You should be able to run screws up to 1" into them without fear of encountering wiring. If wiring is closer to the surface it should be protected with steel plates.

You can try using a non-contact voltage sensor, but my guess is that results will be nebulous with so much electrical whatnot happening right there. Instead, locate the studs accurately and only drill there. Go slowly and observe the debris. If it isn't wood that you find immediately behind the drywall, do not proceed.

Ignoring the comments by other users regarding safety concerns (as I'm not knowledgable with such things or aware of where you are in the world), if you still wanted to mount your coat hook rack without drilling any screws etc, you could use adhesive strips. There are certain brands that are good because they peel off walls easily, e.g.

https://www.amazon.co.uk/s?k=command+strips&ref=nb_sb_noss_2

You could use these to hang up a rack, or they often come in individual hooks you could hang up, either externally or on the inside of cupboard doors as others have suggested.

Best of luck!