Voltage balance

A voltage balance or potential balance , also known as an absolute electrometer , is a historical test setup and a special design of an electrometer . It is a beam balance whose one load is a capacitor plate . In this way, the electric field force is compared directly with the weight of a known mass. The voltage balance was previously used to measure high electrical voltages or - if the voltage is known - to determine electrical permittivity . Today it is primarily used as a demonstration experiment .

The invention of the measuring arrangement is attributed to the German physicist Gustav Robert Kirchhoff or the British physicist William Thomson, better known as Lord Kelvin , depending on the source .

Measurement setup

If you apply a voltage to the capacitor, you have to put another piece of weight on the scales in order to have the balance.

• Under the capacitor plate attached to the balance, a second plate of the same size is attached in parallel at a short distance.
• The plates are first electrically connected to one another in order to discharge them and guarantee that there is no voltage. A resistor can be used to limit the current. The balance is then tared.
• Now the plates are electrically separated and charged by z. B. connects to a DC voltage source. This creates an electric field between them and the plates attract each other.
• To compensate for the force between the plates, weights are added to the other weighing pan.

evaluation

Illustration of a historical tension balance (around 1870) with a Leiden bottle to stabilize the tension

The following applies to the electrostatic force : ${\displaystyle F_{E}}$

${\displaystyle F_{E}={\frac {1}{2}}EQ={\frac {1}{2}}{\frac {U}{d}}\cdot CU={\frac {1}{2}}\varepsilon _{0}\varepsilon _{\mathrm {r} }{\frac {A}{d^{2}}}U^{2}}$

with the electric field strength , the amount of charge , the distance between the plates , the electric field constant , the relative permittivity of air and the area of ​​the upper plate . The factor occurs because the weighed capacitor plate is only exposed to the field of the other plate, not its own. This is why the effective field strength for a plate is only half as large as the measurable field strength between the two plates. ${\displaystyle E}$ ${\displaystyle Q}$ ${\displaystyle d}$ ${\displaystyle \varepsilon _{\mathrm {0} }}$ ${\displaystyle \varepsilon _{\mathrm {r} }}$ ${\displaystyle A}$ ${\displaystyle {\tfrac {1}{2}}}$

The following applies to the weight of the added mass : ${\displaystyle m}$

${\displaystyle F_{G}=mg}$

with the acceleration of gravity . ${\displaystyle g\approx 9{,}81\,\mathrm {\tfrac {m}{s^{2}}} }$

If the scales are balanced by the additional masses, the torques on both sides have the same amount. With the bar lengths a and b then applies

${\displaystyle F_{E}\cdot a=F_{G}\cdot b}$

and thus:

${\displaystyle {\frac {1}{2}}\varepsilon _{0}\varepsilon _{\mathrm {r} }{\frac {A}{d^{2}}}U^{2}\cdot a=mg\cdot b}$

This results in the relationship for the voltage:

${\displaystyle U={\sqrt {2\left({\frac {b}{a}}\right)\cdot {\frac {mgd^{2}}{\varepsilon _{0}\varepsilon _{\mathrm {r} }A}}}}}$

If the voltage is known, this measuring arrangement can also be used to determine the electric field constant or the relative permittivity of the dielectric .

The above derivation applies to a homogeneous electric field between the plates. Inhomogeneities mainly occur at the edge. To prevent these from falsifying the measurement result, the upper capacitor plate is extended by a protective ring that surrounds it concentrically and has the same distance from the lower plate. It is at the same electrical potential as the top plate, but is not attached to the arm of the beam balance. As a result, the inhomogeneous marginal fields appear on the outside of the protective ring. The space above the weighed plate should be as free from fields as possible. It is therefore advantageous to choose the earth potential for this and the lower plate to deviate from it. The effective stress depends on the contact stresses and the work function on the plate surfaces . High voltages reduce the resulting measurement errors. ${\displaystyle U}$

Web links

• Using the principle of the voltage balance to represent the volt (p. 61) or as a possible approach to redefining the kilogram using the Josephson constant (p. 50)

Individual evidence

1. ↑ Lexicon of Physics at www.spektrum.de, accessed on August 3, 2017
2. ↑ Gradewald, Rudolph (Ed.): "Grimsehl Textbook of Physics. Volume 2: Electricity", 21st edition, Springer-Verlag, Heidelberg 2013, p. 57
3. ↑ Richard Becker, Fritz Sauter: Theory of Electricity: Volume 1: Introduction to Maxwell's theory . 21st edition. Teubner, Stuttgart 1973, ISBN 3-322-96790-5 , p. 64 .