  In the presence of shot noise the charge on a mesoscopic conductor
fluctuates. We are interested in the charge fluctuations which arise if the
conductor is in the proximity of a gate to which it is coupled by long range
Coulomb forces only. Specifically we consider a gate coupled to the edge of a
Hall bar subject to a quantizing magnetic field which contains a quantum point
contact. The gate is located away from the quantum point contact. We evaluate
the charge relaxation resistance for this geometry. The charge relaxation
resistance determines the current fluctuations and potential fluctuations
induced into the gate. If there is only one edge channel the charge relaxation
resistance is determined by transmission and reflection probabilities alone,
but in the presence of many channels the density of states of all edge states
determines this resistance.
