Electrolytic Tank Experiment (Mapping electric fields)

Principles

This method has been widely used for decades. Equipotential boundaries are represented in the tank by specially formed sheets of metal. For example, a single dielectric problem such as a three-core cable may be represented using a flat tank different permittivities are represented by electrolytes of different conductivities separated by special partitions. Otherwise, the tank base can be specially shaped. The conductance of the entire model is a scale model of the capacitance of the system being represented, care being taken to minimize the errors.

An electric field, E, exists anywhere a stationary test charge, qo, experiences an electric force, F. E and F are vector quantities and the relationship between them is given by

E = F qo

qo is assumed to be positive and very small. E and F are always in the same direction. Electric field lines are imaginary lines used to visualize electric fields. The lines always leave positive charges and enter negative charges. They are closer together where the field is stronger and they never cross. The lines indicated the direction of the force acting on a test charge placed at that point. If a positive test charge is released in an electric field it will move away from the positive side of the field toward the negative side. The field will do work on the charge as is moves from point A to point B according to

Since the electric force is a conservative force, there will also be a change in potential energy,

ΔU = -W

The change in potential energy per unit charge is a scalar quantity called the electric potential, V. Electric potential is always measured between two points. In any field there exists a set of points between which there is no potential difference. A set of such points will make up an equipotential surface. This surface is always perpendicular to the electric field. In other words, when F and ds are perpendicular, θ equals π/2 and cosθ equals zero. No work is done moving a charge along such a surface.

Electric potential, or voltage, is easily measured. This phenomenon can be used to map an electric field.

In this experiment, the analogy between static electric field and stationary current field is used.

Static electric field Stationary current field

= 𝜀 𝐽 = 𝜅

𝑄 = ∮ 𝑑𝑠 𝐼 = ∮ 𝑑𝑠

𝐶 =𝑄

𝑈 𝐺 =

1

𝑅=

𝐼

𝑈

If the environment between electrodes is isotropic, self-conductivity and dielectric coefficient are constant, therefore current density, J (in stationary current field); and electric field, E and electric flux density, D (in static electric field) will be in the same direction. Thus, current density and electric field lines overlap. This means, in an electrode system, if a conducting material is placed instead of dielectric between electrodes, equipotential lines will remain the same. For that reason, by electrolytic tank method, equipotential lines are determined after that current density lines i.e. electric field lines can be determined by using electric field lines and equipotential lines are orthogonal (always perpendicular).

Experimental setup

Principle: static electric field has an analogy with current field.

To voltage source

Current lines Flux lines analogy

U

R1

A

R2

~ A A

Model

electrodes

Ammeter

Probe

Model

electrodes

Electrolitic

liquid (?)

Bridge measurement

Experiment

1. Place scaled model of electrode system to be analyzed in electrolytic tank. 2. Put electrolytic liquid (tap water is conductive because of chlorine) in the tank. 3. Draw the electrodes on a graph paper. 4. Set the potential of the probe by changing resistors from 10% U to 90% U by 10% steps while

keeping total resistance 100 kΩ. 5. When you have the same voltage at the point A and the probe, the system is balanced (no

current, no light, no sound, … ). That is a point on the equipotential line. 6. Record at least 10 points for each potential value on to your graph paper.

Questions

1. Draw equipotential lines and electric field lines for your electrode system. 2. Determine maximum electric field strength and total capacitance of your electrode system

experimentally (refer to next page for equations) and theoretically. 3. Why AC is preferred to DC in this method of plotting equipotential curves? 4. What other liquids could be used instead of tap water? Give examples. 5. How is a multilayered electrode system represented by using this method? briefly explain.

R3

𝐼 =𝑉𝐴 − 𝑉𝐵

𝑟𝐴

rA

R1

A

R4 R2

VA VB

R1

A

R2

U

𝑉𝐴 = 𝑉𝐴 → 𝐼 = 0

In case of balance:

Current through

ampermeter

𝐼 =𝑈

𝑅1 + 𝑅2

𝑈2 = 𝐼𝑅2 =𝑅2

𝑅1 + 𝑅2𝑈 = 𝑈𝐴

Electric field and equipotential lines with two different electrodes configuration

Equations related to experiment

d: the thickness of the electrode [d = 1 cm]

m: number of equipotential lines

n: number of electric field lines

b: width of one cell

a: height of one cell [create square cells when drawing the mesh b/a = 1]

insulation between electrodes is air

∆∅ =𝑈

𝑚 + 1

𝐸𝑚𝑎𝑥 =∆∅

𝑎𝑚𝑖𝑛

𝐶 =𝑄

𝑈= 𝜀 × 𝑑 ×

𝑛

𝑚 + 1×

𝑏

𝑎