Qfyilyi

Below are photos of two scope probes with different ground clip lengths:

I have read that the shorter ground is used to minimize the inductance of the probe ground lead.

But what does that help for? What happens when the inductance of the ground lead is low? What kind of interference it prevents?

It doesn't prevent interference. It prevents ground lead impedance.

Simply imagine an inductor in series with your ground connection: that acts as a low-pass filter. So, high-speed currents can't be grounded, and for these, your instrument seems to float.

I was invited to assist in debugging a switching regulator IC; problem was "two kinds of oscillation".

I asked what were the frequency of oscillation, and answer was 80MHz.

I asked "how long is the scope ground lead" with answer being "The usual 6inches or 8inches".

I explained "The resonant frequency, of 200nH (8") gnd-lead scope probe with 15pF input capacity, is about 90MHz."

Turns out the silicon designer had cranked out LDOs in his prior IC work, and had never needed to learn fast transient probing methods. Here he got to learn about scope probe ringing.

The other form of oscillation/noise/weird-behavior involved jitter in the timing of entering and exiting discontinuous modes. That involved very very slow decays of the regulated voltage and timing errors caused by thermal noise.