Most currents around here come in tens-of-milliamps, maybe a few hundred, tops, but it’s worth noting some curves from the Tektronix AM503 current amplifier manual for A6302 Hall effect probes:
The maximum current drops from 20 A for frequencies above 20 kHz:
There’s a 100 A·μs pulse charge limit:
Because the probe is actually a pulse transformer, its internal termination imposes a (small) load on the input circuit:
The specs are 100 mΩ at 1 MHz and 500 mΩ at 50 MHz, which means the load is essentially zilch for the circuits and signals I deal with.
The Tektronix Probes for Current Measurement Systems has some useful descriptions.
Memo to Self: Should any of those limits matter, rethink what you’re doing.
An interesting story about the AM503 design from someone who lived through it.
The Smell of Molten Projects in the Morning 