How far can an arc travel outside a box. I have a suspicious fire I am investigating where it appears that above the breaker box there was an arc that supposedly traveled outside the box and ignited a box of styrofoam cups sitting in boxes on the floor below the breaker box. Could this have happened this way??

1. You are investigating a fire? Has some other investigatory agency told you about the apparent arc? If so, what did s/he say about how and if it could have happened that way? And did they confirm that this area is the origin of the fire?

2. How far is the box from where the cups were?

3. Is this issue for help with a homework or other study issue?

NO WAY would an "arc" travel that far. Especially from metal to styrofoam.
Molten metal could however have fallen into the cups, but it is highly unlikely that there would be enough to actually ignite styrofoam.

Here is more than anyone would want to know about arc blast from IEEE:

http://www.ieee-pcic.org/archive/The%20other%20Electrical%20Hazard%20%20%20Electric %20Arc%20Flash%20Burns.pdf

I think it is very possible for this event to happen, under certain likely conditions.

If there is an open knockout, or any other poor fitting panel cover or missing circuit breaker, a short circuit could eject enough melted material and plasma spray onto the cups.

Or perhaps a short at a cable connection at the top of the panel, less likely, but possible.

A short of this nature will produce noticeable damage at the point of short.Need to closely inspect the panel.

Sounds malicious - arson?

No arc.
Possibly molten metal from a short, but how would the sparks/molten metal beads get out?

Lightning?