I would like to build a monopole antenna with a loading coil for HF frequency of 3 MHz. The monopole arm is 60 cm long and the coil should be at the base.

So, using a 570 µH loading coil should work for that monopole?

I need the antenna only for receiving.

I am trying to make a ground plane monopole for SW reception. I thought choosing 3MHz would let it receive up to 30 MHz too. But if I target it for 15 MHz then would it have a range to cover from 3MHz to 30 MHz?

So, using a 570 µH loading coil should work for that monopole?

Define "work": I haven't done the math myself what an appropriate loading would be for a thing wire antenna of 1/41.666… of quarter of a wavelength (the length at which an unloaded monopole would be resonant).

It will be impossible to give a precise value here, because at a 100m wavelength, the house your operating this in, the transmission line mantle, your electric wiring, water plumbing, car in the driveway will all couple into the same field, and can pose an inductive or capacitive parasitic load to an antenna.

Also note that this way of modifying an antenna does make it a relatively narrowband antenna; only for the small frequency range where the loading and the capacitive effect of being electrically short cancel out, you get the effect you meant to get with your loading; everything outside that would get filtered out. Now, there's no amateur bands at exactly 3 MHz, and I don't think there's a broadcast band there anywhere on this world, either. There's airplane comms happening at 3 MHz, in a ca 300 kHz wide bandwidth (2.850 MHz to 3.155 MHz). So, if you want to get that airband, you will need an antenna that can be used for 30% of its center frequency in bandwidth! That precludes a narrowband technique like an inductively loaded electrically extremely short monopole.

But even if it worked perfectly, it will not change that the effective area of a monopole that is this tiny compared to the wavelength is really really small, and you won't get enough signal out of it.

A monopole shortened this drastically is the wrong approach to receiving.

Look at the typical broadcast radio receiver for so-called Shortwave Radio. They're not monopoles! They are either large outdoor dipoles, which come into the order of magnitude of the wavelength (so that loading makes sense). Or, they are loop antennas; the classical "frame" loop antenna (which is the diamond shape you see in so many Ham Radio logos), or a rod antenna.

But before you design your antenna any further, you really need to figure out which range of frequencies you need it to cover. The center frequency doesn't suffice (as I've been saying under multiple of your questions…), you need to state which frequency ranges you need to cover. And as already said multiple times, if this is hard to figure out for you, just tell us what you want to really do with it, instead of asking questions based on incomplete requirements; we can help you with the requirements. (I should have checked your user account before I wrote this lengthy answer.)

• I am trying to make a ground plane monopole for SW reception. I thought choosing 3MHz would let it receive up to 30 MHz too. But if I target it for 15 MHz then would it have a range to cover from 3MHz to 30 MHz? Commented Aug 1 at 5:27
• No it wouldn't. What range do you really need to receive? Because an antenna that works well from 3 to 30 MHz antenna is what we would call an ultrawideband antenna. It would be huge, expensive, and heavy. You can only build compact narrowband antennas, i.e. antennas whose frequency range is small compared to the middle frequency. That's why for such low frequencies, you tune your antenna to the actual frequency you want. In other words, there's no one antenna that does all, you need to have the antenna be adjustable if you really need to cover 3 to 30 MHz. Commented Aug 1 at 10:17
• But you really don't want to cover 3 to 30 MHz in a practical application (unless it's regulatory or military spectrum surveillance, in which case you wouldn't build yourself, but buy a calibrated, expensive, heavy, and large set of wideband antennas and switch between these for multiple bands within that huge 10× frequency range). Narrow down your application from "want to receive SW" to what you really want to receive – is it the shortwave broadcast AM band? The aeronautical band? The maritime bands? Atmospheric resonance experiments? Commented Aug 1 at 10:18
• I need to make a compact one for HF. If HF can't be received using small antennas then why do small AM radio receivers come with a whip antenna of 60cm only? Commented Aug 3 at 14:03
• because, and I repeat that again, these antennas are both bad antennas, and tuned antennas. and, I'm not sure, because I haven't seen a receiver with a 60cm whip in eternity, but I think you might be referring to the antenna used for UHF reception, whereas the HF reception happens with a tuned ferrite rod loop antenna in the case Commented Aug 4 at 10:07

I agree with some of the other answers that this antenna system will have performance issues, especially compared to the antennas that are typically used for amateur radio stations. However we know of portable shortwave receivers with short whips, so it can work to some degree (of course they likely have a much different design)

If you want to get experience in antenna building and experimentation, and particularly if you have a nanoVNA where you see what is gong on, I would encourage you to try it out to see what happens. The nanoVNA will show you the resonant frequency, bandwidth, impedance, etc.