# How to measure a static electric field?

I looked up google but didn't find any design for measuring electric field that doesn't vary with time.

My own idea is to use two parallel plates (like a capacitor but without the dielectric). In an electric field E a potential difference V = Ed (d is separation between the plates) will develop, which can be measured using a voltmeter. Will this work?

An old method to measure an electric field does, ideed, use two thin metal plates of area $A$ held on insulating handles. These metal plates are put in contact and the combined plates are inserted into the electric field so that the surfaces are normal to the field lines. Then a (positive and negative charge) of $Q=A\sigma$ will be induced on the upper and lower plate where $\sigma=\epsilon E$ is the induced charge per unit area on the upper and lower plate, $\epsilon$ is the total permittivity of the surrounding medium. One can then separate the two plates and measure the total charge $Q$ on one of them with a Faraday cup electrometer. The electric field strength is the given by $$E=\frac{Q}{\epsilon A}$$

Measuring the static voltage on a capacitor with a voltmeter is, in general, not a good idea because you will get a transient discharge current through the voltmeter.

• Could you clarify how Q should be measured? Wikipedia tells me a Faraday cup electrometer is used to study aerosols, so how does it apply here? Jan 15, 2018 at 6:48
• @DangerousTim - If you take the charged plate and insert it into a Faraday cup (that's just an open metal vessel where your plate fits in) all the charge will be transferred to the cup and measured in an connected electrometer. Jan 16, 2018 at 2:33

You can't measure the voltage between two plates in a static electric field because the field will also exist within the wires of you meter. You need to rotate the plane of the plates and use slip rings to feed the voltage to an AC meter. As I recall, there is often a vertical electric field near the surface of the earth, but it usually does not produce noticeable effects.

According to this source, there are electric field probes based on three orthogonally placed dipole antennae. Such probes have applications ranging from measuring radiation levels in fields to satellite detection of earthquakes.

A dipole often orients itself in the direction of the electric field.

Thinking something wild here, a detector you could carry; in theory, you should be able to measure static electric field using a light charged metal wool in a glass sphere: