Final answer:
The rule of thumb for changing mA to maintain density is based on the relationship that current density is proportional to current and inversely proportional to the area. Adjustments in mA must be compensated by inverse adjustments in cross-sectional area to keep the density unchanged.
Step-by-step explanation:
The rule of thumb for changes in mA to maintain density is that the current density is proportional to the current and inversely proportional to the cross-sectional area through which the current flows. If we have an increase in current (measured in milliamperes or mA), maintaining the same density would require an increase in the area. Conversely, if we decrease the current, to maintain density, we would need to decrease the area.
For example, if the current supplied to a lamp with a 100-W light bulb is 0.87 amps and the lamp's wire has a diameter of 2.588 mm (10-gauge), the magnitude of the current density can be calculated. Should we wish to change the current by a certain factor to maintain the same density, the area of the wire would have to change inversely by the same factor.
When considering problems like the proton accelerator that produces a beam with a current of I = 9.00 μA and a given radius, the current density can be found which helps in understanding the behavior of charged particles in the accelerator.