Lecture - Measuring conductivity：讲座——电导率测量.doc

Ion counters measure the concentration of small ion charge carriers in the air (as we will see they can only measure one polarity of charge carrier at a time).? A conductivity meter measures the airs conductivity.? And, actually, it isnt able to measure the total conductivity because both positively and negatively charged small ions make the air conductive.? A conductivity meter is only able to measure the contribution that small ions of a single polarity make.? Ions counters and conductivity meters often make use of the cylindrical capacitor geometry shown below.? The outer electrode is connected to plus or minus voltage V, the inner electrode is grounded. If we assume that we are looking a just a small section in the middle of a much longer cylinder, the E field will have just a radial component, Er.? The solution above, obtained using Gauss Law, is the same as the field around an infinitely long line of charge with uniform line charge density.Next we will try to find an expression for the electric field in terms of the potential difference between the two cylinders. If the outer cylinder is connected to positive potential, the grounded inner cylinder will have negative charged induced on it.? The E field will point inward as shown in the figure above.? It is a relatively easy matter to determine the capacitance Lets look first at how an ion counter works.? An ion counter will measure the concentration of small ions in the air. The electric field will cause a? positively charged small ion entering the cylindrical capacitor at the left to drift toward the inner conductor with a drift velocity (vd).? In time dt, the small ion will drift dr (Point 1).? The drift velocity, Point 2, is just the electrical mobility, Be, times the electric field.? T at Point 3 is the time it will take the small ion to drift from the outer cylinder to the inner cylinder. Now in order to be counted the small ion must make it to the center conductor before it travels a distance L,