How to detect a magnetic field going over a coil?
If you are looking to see an induced voltage on the coil when the magnet moves over it you may find that you need higher speed. Induced voltage is proportional to speed and therefore if you move it slowly, your oscilloscope may not see the tiny change in induced voltage.

If your coil has only 4 turns this won't help pick-up the movement. Induced voltage is proportional to number of turns so try winding with a hundred turns to see what you get.

Alternatively, if you set up a free running oscillator that uses the coil inductance and move the magnet towards the coil, the material (not the magnetism) that forms the magnet will alter the field pattern produced by the oscillator and you may see a change of frequency.