Can I use I2C over 2m cables?
I2C is not designed to be used over long distances but I know of several applications where it is actually used over a distance of about 2 meters.
I also know of one case where they had issues with that and it was eventuelly fixed by fixing ground loops I believe.

To be sure that it will function, you should use an I2C bus extender like the P82B715.

However, the datasheet of the PB2B715 says the following in section 8.2:


  For typical twisted pair or flat cables, as used for telephony or
  Ethernet (Cat5e) wiring, that capacitance is around 50 pF to 70 pF /
  meter so the cable could, in theory, be up to 50 m long. From
  practical experience, 30 m has proven a safe cable length to be driven
  in this simple way, up to 100 kHz, with the values shown. Longer
  distances and higher speeds are possible but require more careful
  design.


So the experts (NXP is the former Philips, the inventor of I2C) say that 30 meter has been proven a doable distance.  My experience says 2 meters is a doable distance, and experiences that were reported back to me indicate that more heavily loaded I2C buses without any extender are also possible.

The key points to working I2C buses on long distances are:


Using a low capacitance cable (twisted-pair/Ethernet);
Limiting the bus speed;
Having pull-ups that are correctly sized.


Pullup calculation

Texas Instruments has a good application note (SLVA689) about pull-up calculation .


The lower bound of the pullup (minimum value) is determined by the current the weakest peripheral on the bus can pull, and the maximum voltage that represents 0 for any peripheral.  So if 1V is still 0, your VCC is max 3V6 and your weakest device can only pull 20mA, your resistance is determined by the voltage loss over the resistor and the current pulled by that device: \$(3.6\ \mathrm{V}- 1\ \mathrm{V})\ /\ 20\ \mathrm{mA}=130\ \Omega\$ .
The upper bound is determined by the maximum rise time: your maximum I2C frequency is directly related to that, but there is also an upper limit defined by the protocol.  The upper limit is \$R_{max}=t_r/(0.8473 * C_b)\$ .  Where \$t_r\$ is the maximum rise time and \$C_b\$ is the bus capacitance.  So if \$C_b\$ is 400pF, and the bus is operating in standard mode (\$t_r\$=1ms), then you'll find \$R_{max}=2950\ \Omega\$ .  TI's application note has graphs so that you can find appropriate values quickly.
Of course the value for the pullup is the equivalent value of all pullups in parallel combined.  You may have a pullup on the master end, the slave end, and any other slave/master on the bus.
The more you are "at the limit", the more you also need to account for "parasitics" such as the voltage drop in the cable.