ELECTROSTATICS

Charge is one of the powerful natural phenomenon that underpins our existance.

Charge governs the ATOM - chemistry is all about charges interacting - bonding.

At the bottom of the heap ranging from thunderstorms to solar storms lie the elementary charged particles

- the PROTON and the ELECTRON.

NAMES - some of many

Charles Coulomb - showed the elementary force relationship between charges back in about 1780.

J.J Thomson "discovered" the electron using a primitive mass spectrometer invented by himself in 1897.

Robert Millikan - by sensitively measuring the motion of droplets of oil, measured the charge on a single electron in about 1920.

The unit of charge is named after Coulomb but is actually far too large a value to be a realistic unit in a lab. It is nowadays defined from electric current using magnetism.

The smallest observable charge - that of electrons, protons and other elementary charged particles is "e" = 1.602 x 10^-19 coulomb. ( There is one smaller charge - that of a quark - 1/3 of "e" - never been seen!!!)

Coulomb's Law

Universal Law of nature describing how any two spherical charges affect each other. The law operates at nuclear and Van de Graaff generator levels.

F = 9x10⁹ Q₁Q₂ / r²

Notice that this is very like Newton's Law of Gravity. Notice that each charge is mentioned - "F is the force acting on each Q at a distance of r "

When we have lots of charges affecting one other, then

• calculate each force by Coulomb's Law on the charge
• use vector addition to get the total force on that charge.

Electrostatic Fields

Usually there are LOTS of charges around the place - typically 10 ¹⁵ of them giving total charges of about 1 microcoulomb. These can be spread over surfaces so what happens is that the maths of Coulomb's laws gets very messy. Instead we look at the total "field" of the charges - the total effect in space on a TEST CHARGE.

"TEST CHARGES" are little charges moved around in places to see if they receive an electrostatic force. If they do, then an Electrostatic Field is said to exist there. It is rather like putting a "test finger" in a bath of water to see if it is too hot to get into.

If an "E field" exists, then it can be used to calculate the effect of all those charges that created the field on any free charges like electrons or protons or smoke particles.

The defining statement is

E = (defined by) Force on test charge / size of test charge we always ASSUME a positive charge

E = F / q so F = qE is the statement about how a charge feels in a known Field strength.

This is a definition so it works EVERYWHERE - this is useful because we can calculate E often if we know Potential Difference ( in volts ) - all we need is a voltmeter!

Much more limited is the formula which we get by combining Coulomb's Law with the above definition for the field of one charge.

We get for one SINGLE spherical charge E = 9x10⁹ Q / r² - Q CREATES E at the distance r.

If we have lots of charges, we must use vector addition of each field to calculate the field value at different places.

Uniform E fields are particularly interesting because charges move in "projectile motion" parabolas. The maths is identical even though the numbers are very extreme. Typically electrons move at 10⁷ ms^-1 and accelerations are 10⁺¹⁵ ms^-2.

Energy in E Fields

When a + charge is moved near an area of + charges, it gains potential energy in the same way a weight lifted gains E_p. The weight gains gravitational Ep, the charge gains electrostatic E_p. When released, the charge loses that E_p and might gain kinetic energy. ( see Fields Tute )

We DEFINE POTENTIAL DIFFERENCE ( PD ) also known as "voltage" between two places in the field, as

PD = V = E_p between the two places for our test charge , q
value of q

thus E_p = q V

Very simply that means if we know the PD measured with a voltmeter, we can work out how fast a charge will end up - eg for an electron gun in the back of a TV set.

eg. A PD of 15 000 volts in an electron gun will provide an electron with a speed given by

qV = 1.602 x 10^-19 x 15 000 J = 2.4 x 10^-15 J = 1/2 mv²
As the mass of an electron is m = 9.11 x 10 ^-31 kg , we manipulate to get v = 7.26 x 10⁷ ms^-1

Field Strength & PD

When we use the definition of

Work Done = Force x distance = change in energy x distance

we can replace "Force" by qE

WD = qEd d = distance

WD = Change in energy = qEd SO Change in Energy / q = Ed

BUT this is the definition of PD

V = Ed or E = V / d

Electrostatic Field Strength = "Voltage" / distance between measuring points.

Go to POTENTIAL ENERGY IN RADIAL FIELDS for Gravity and Electrostatics