On the General Theory of Electrometer Design

It is shown that Brownian motion sets a lower limit on the smallest charge detectable. This limit is approximately ${\mathrm{(kTC)}}^{\frac{1}{2}}$ with k Boltzmann's constant, T the temperature, and C the capacity of the system in centimeters. A discussion of the difficulties of reaching this limit with a vacuum tube electrometer is given with particular emphasis on the problem of shielding in which connection several suggestions are made. The ordinary electrometer is treated in much greater detail. A general theory of all electrometers is developed and it is shown that this theory together with various practical desiderata virtually dictate the essential features of the design of an electrometer. An electrometer of the design proposed will reach the limiting useful sensitivity; the quarter period when at this sensitivity is ${\text{(πδθ/2)(I/2kT)}}^{\frac{1}{2}}$ where δθ is the least detectable change in angle of the suspended system and I is the moment of inertia. Without resorting to extreme construction this time can be made as short as fifteen seconds and it can quite possibly be further reduced by a factor of one thousand. An electrometer of the proposed design will have a zero independent of temperature, battery voltage, and slight vibration. There are two adjustments which are noninteracting and any desired sensitivity can be obtained in a simple and straightforward manner.