Electrostatic analyser at the path of 14C+ beam is necessary to definitively filter other ions, which eventually passed through the analysing magnet. These might be e.g. lighter carbon ions which, due to multiple charge changes, accidentally got higher energy in the accelerator. Due to that, 14C detector is reached almost solely by the ions of 14C.
Some ions of 12C and 13C going out of accelerator can pass through the analysing magnet along the 14C trajectory. These might be ions which due to multiple charge changes got higher energy in the accelerator. Though the probability to get the desired energy is extremely low, it may be significant with respect to the very low number of 14C atoms.
In electrostatic analyser, charged particles undergo electrostatic force, which bends their trajectory. The bending radius depends on particle energy and charge, but is independent of its mass. Due to that the ions of abnormal mass (i.e. different than 14), which had to have energy (or charge) adequately abnormal to pass the analysing magnet, are not able to penetrate the electrostatic analyser.
Animation below: illustration of the electrostatic analyser operation.