Gold Leaf Electroscope.....
Coulombs Force Law.....
Electric Field .....
Energy Stored in A Capacitor..... Force of Attraction between plates..... Dielectric Strength..... Table of relative permittivity.....
Comparison between Electromagnetic and Electrostatic variables.....
Electrostatics is the study of the electrical fields surrounding electrical charges and the resulting forces
between charged surfaces. The resulting interactions are entirely dependent on the
charges and their relative positions and not by their motion.
C = Capacitance (farads)
Gold Leaf Electroscope
An electroscope is a device to determine or measure the presence of electrostatic charges. The device's operation is simply based on the Coulomb Force Law. This is a relatively crude instrument used only for education. Modern instruments, based on vacuum tubes or solid state technology can be used to measure extremely small charge levels.
Two gold leafs (A) hang from a metal rod (B) within a metal container D. The top of the rod supports a conducting disc C (or a sphere). The rod is supported in a highly insulating stopper (E).
If the gold leaves become charged, because each leaf
is equally charged , the leaves repel each other.
First the electroscope is earthed. A negatively charged object is moved close to the electroscope system causing a separation of charges the -positive charges moving towards the charged objects and negative charges moving to the gold leaves causing them to separate. If the electroscope is earthed without moving the charged objects then the negatively charges flow to earth. If the earth and the charged objects are removed the positive charges distribute over the electroscope system...
Physical contact by a charged object causes a flow of charge into the electroscope. This is used to identify that the object is charged.
A charged point is surrounded by an electric field which are effectively lines of force radiating outwards. The conventional direction assumed for these lines of force are from positive charge to negative.i.e the lines indicate the force experienced by a positive charge . The lines of force never intersect and therefore any charge will experience a force in one direction at any location.
The forces of attraction and repulsion acting on adjacent charges will cause a charged surface to be evenly distributed with lines of force radiating outwards as shown in the two examples below
If the space between the surface allows any sort of conduction the charges will tend to
migrate across the space and neutralise itself.
C = Q/V... or Q = CV
The strength of the force experienced by a unit charge in a field is called the field
strength (also called the electric stress) . This is measured in
newtons per unit charge and is represented by Ε
Ε = V /d volts per metre
The lines of electrical force are called the flux of the system . The flux is measured in coulombs i.e a charge of Q coulomb creates a flux of Q coulomb. The flux passing through a unit area is called the flux density D
D = Q /A coulombs per metre 2
The permittivity of free space in a vacuum is the ratio of flux density to the electric field strength and is easily obtained as follows
If the material between the plates is not a vacuum then the ratio ( D / E)is is different to the permittivity of free space and is generally identified as ε ( absolute permittivity). The absolute permittivity equals ε o.ε r where ε r is the relative permittivity. Different values of relative permittivity are tabled at the bottom of this page...
Coulomb Force Law
All bodies are able to take a charge of electricity and this is termed static electricity. The charge on a body
is measure by means of the force between the charges.
Note: a negative force results if the points have opposite charges and a positive
force results if the points have the same polarity
If the space between the charges is another material or air the law may be written
εr relative permittivity of material. The value of k will also be different if the separating medium is not a vacuum or air.
A physical capacitance is often made up of plates insulated from each other by insulating materials selected to be able to withstand high voltages. This insulating material is called the dielectric. The capacitance is directly related to the permittivy of the dielectric and the area of the plate and is inversely related to the distance between the plates. The rating of a plate capacitance is given below
If the capacitor is a multi-plate type then the capacitance is simply the capacitance of one plate multiplied by
the number of paired plate faces. i.e a n plate unit would have capacitance of a two plate unit x (n-1)...
The capacitance of two co-axial cylinders is calculated as follows.
Let Q be the charge per unit length of cylinder.
Energy stored in a Capacitance
Assume there is a p.d. across a capacitance of C farads which is increased
from v to v + δv
The energy per cubic metre for a capacitor with an plate area A and a dielectric thickness d =
Force of attraction between oppositely charged plates
Consider two plates are separated by distance x in a medium of absolute permittivity ε each plate having an area A.
If the p.d between the plates is V then from the equation above the energy per cubic metre of dielectric =
Assume one of the plates is movable as shown .
The force of attraction between the plates is 0,5.ε.A .(Voltage Gradient)2
The dielectric material can withstand a certain potential difference. If the pd is increase above this value there is a high risk that it will break down. This potential difference is called the dielectric strength. Capacitors made with high dielectric strength materials can have higher capacity because the dielectrics can have lower thickness for the same voltage rating. Typical dielectric strenth values are provided below..
Table show relative permittivity for different materials
Note: the permittivity of some materials varies with the frequency of the applied voltage.
Comparison of Electromagnetic and Electrostatic Variable names and Symbols