50Hz hum on oscilloscope probe only when using clip
The ground wire on the probe with a 10M 10:1 probe still creates a loop antenna.  To reduce the area of the loop, use two test pins &lt;1cm apart and remove probe "antenna" ground wire and only use the tip and ground barrel for measurements.

If the noise still exists when you probe the ground, twist the scope cable to raise CM impedance and better, use a large ferrite choke around the probe cable.  For even better results , calibrate two probes , twist both together, keep at right angles to stray current paths, remove ground and probe tips and calibrated to match perfectly ona scope test square wave then use Ch2 Invert and add Ch1&amp;2 to get a perfect flat line, then verify probing ground near noisy source with barrel grounded to same ground pin and use large ferrite torroid or clamshell choke around both cables

This is the best you can do without more expensive active diff probes.

when using Ch 1 Invert, ensure both channels have calibrated gain in desired gain range and do not saturate either channel when using a Differential Probe method of scoping, other difference errors result.


when you have imbalanced probe high Z , within high voltage E fields, your body can and does absorb stray E field (high V but low power) and shunt to ground,, thus you can improve apparent readings.