If the confining potential of electrostatically trapped electrons fluctuates, then the number of trapped electrons also fluctuates. The linear relationship between potential fluctuations and the number of trapped electrons is investigated, considering two loss mechanisms for a nearly collisionless plasma: (1) small‐angle collisions (diffusion), and (2) large‐angle collisions. This nearly collisionless model predicts the line tying of interchange modes in a mirror‐trapped plasma is orders of magnitude larger than previously thought for a fusion plasma, yet still not strong enough to completely line tie an axisymmetric mirror. Also, a nonlinearity in the response can occur at low amplitude.