Building a powerful electromagnet for repulsion

Question

I have to make an electromagnet for my project. The role of the electromagnet is that I want it to repel a permanent magnet so that its hard to press down at that point an N42 ring Neodymium magnet (Outer diameter 26,75 mm: Inner diameter 16 mm: Height 5 mm) from around 2-3 inches distance. So that if a pulsing voltage is provided to it, it makes a vibration to be felt by permanent magnet.

EDIT

I have now some results to talk about.

I bought few EM from market but they are too weak for this purpose probably not built for repulsion purpose. I have made 4 electromagnets so far with different specifications and have positive results. Now I want to get some feedback for what now on I am thinking to do based on what results I got so far.

Here are specifications & results of my 4 build EM:

I used Ferrit core of diff dia and height and enameled copper wire of diff dia. To give repulsion from more distance, I put a permanent NeoDem-magnet on top of core. It provided more distance for repul and finished attraction of core to magnet. Total distance of repulsion that felt becomes once I provide power to EM 30-35 mm with diff repulsion push from diff EMs, so 30 mm by permanent magnet that i put on the core and added 5-7 mm by EM. Under is a table listing specifications of core and wire & then how much repul each give to permanent magnet on switching ON/OFF EM.

From these results, I concluded going for core with more diameter and using wire of 1.0 mm is way to go. Now I am thinking to use more thicker core i.e. 4cm, 6cm, and may be 8cm. I have few questions regarding this:

1. Is there any formula or online tool available to calculate what size core with what size wire is optimum or is any rule to make maximum powerful magnet. I am thinking like there may be a saturation point so to use more thicker core than that has no effect or adding more turns only add resistance. There is one available but that is for air core online electromagnet calculator. It's very helpful though for finding resistance of coil and number turns.
2. Any suggestion based on these results for what I am planning to do next will be very helpful.

Answer 1

In my experience (using magnets and designing metal detection equipment), 3 inches is a very long way for coils that might only have a diameter of about 1 inch.

At 3 inches, if you used two similar magnets can you detect the repelling force (or attracting force)? If not then you cannot expect an electromagnet to produce anything like the same magnetic field so it won't work at that distance.