On a 15 cm PCB, where the MCU is on the one end and the current sensor on another, where should R and C components of a passive low pass filter between them be placed? Will the placement affect anything?
I assume you are reading the analog signal of your sensor using the analog to digital converter of your microcontroller, right?
If so, place the RC filter close to the ADC. That way the filter will also be effective filtering out all the noise that you've picked up over the long trace.
If signal integrity is a concern and the analog signal has a high impedance you may also want to put an opamp configured as a voltage follower just behind the sensor. That way the signal over the trace has low impedance and is less prone to noise pickup.
If your MCU has analogGND pin, tie bottom end of the Capacitor to that MCU pin. If your MCU has differential inputs, tie the (-) input pin to bottom of the Capacitor. Bring the Resistor right up against the Capacitor, that node tied to the ADC input pin. A tiny PCB region is the goal, so cellphone energy and fluorescent light spikes have minimal parallel-plate-capacitor target to couple into.
Perhaps use several resistors in series, with ground plane under the resistors to provide additional filtering, effective at RadioFreqs.