Will A Logarithmic Potentiometer Linearise A Capacitor Charge Curve?
Setup a circuit like this to charge your capacitor:



With the circuit values shown this will produce a linear ramp of capacitor voltage from 0V up to 4.4V over a time span of 7 msec.



The pulse source in the schematic provides the reset for the ramp voltage holding it initially at GND. You can repeat the ramp by driving the NPN base high for a short pulse to discharge the capacitor to GND. The ramp will then begin again when the NPN base goes low and the NPN shuts off.

Timing of the ramp can be adjusted by changing the value of R1 and/or C1.