Static Electricity
In the preceding chapters, we concerned ourselves exclusively with electriccurrent i.e. electric- ity in motion. Now, we will discuss the behaviour of static electricity and the laws governing it. In fact, electrostatics is that branchof science whichdeals with the phenomena associated with electric- ity at rest.
It has been alreadydiscussed that generally an atom is electrically neutrali.e. in a normalatom the aggregate of positive chargeof protons is exactly equal to the aggregate of negative chargeof the electrons.
If, somehow, some electrons are removed from the atoms of a body, then it is left with a preponderance of positive charge.It is then said to be positively-charged. If, on the other hand,some electrons are added to it, negative chargeout-balances the positivecharge and the body is said to be negatively charged.
In brief, we can say that positive electrification of a body results froma deficiency of the electrons whereas negative electrification resultsfrom an excess of electrons.
The total deficiency or excess of electrons in a body is known as its charge.
Absolute and Relative Permittivity of a Medium
While discussing electrostatic phenomenon, a certain property of the medium called its permittivity plays an important role. Every medium is supposed to possess two permittivities :
(i) absolute permittivity (e) and (ii) relative permittivity (er).
For measuring relative permittivity, vacuum or free space is chosen as the reference medium. It has an absolute permittivity of 8.854 ´ 10-12 F/m
Absolute permittivity e0 = 8.854 ´10- F/m
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Relative permittivity, er = 1
Being a ratio of two similar quantities, er has no units.
Now, take any other medium. If its relative permittivity, as compared to vacuum is er, then its absolute permittivity is e = e0 er F/m
If, for example, relative permittivity of mica is 5, then, its absolute permittivity is
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e = e e = 8.854 ´ 10-12 ´ 5 = 44.27 ´ 10-12 F/m
Laws of Electrostatics
First Law. Like charges of electricity repel each other, whereas unlike charges attract each other.
Second Law. According to this law, the force exerted betweentwo point charges (i) is directly proportional to the productof their strengths (ii) is inversely proportional to the square of the distance between them.
* Coulomb is better known for his law which states that the force between two point charges is propor-
tional to each charge and inversely proportional to the square of the distance between them.
4.1. Electric Field
The region in which the stressexists or in which electricforces act, is called an electric fieldor electrostatic field.
The stress is represented by imaginary lines of forces. The direction of the lines of force at any point is the directionalong which a unit positivecharge placed at that point would move if free to do so.It was suggested by Faradaythat the electricfield should be imagined to be dividedinto tubes of force containing a fixed number of lines of force. He assumed these tubes to the elastic and having the property of contracting longitudinally the repelling laterally. With the help of these properties, it becomes easy to explain (i) why unlike charges attracteach other and try to come nearerto each other and (ii) why like charges repel each other [Fig. 4.4 (a)].
However, it is more common to use the term linesof force. These lines are supposed to emanate from a positive charge and end on a negativecharge [Fig. 4.4 (b)]. These lines always leave or enter a conducting surface normally.
4.1. Electrostatic Induction
It is found that when an uncharged body is broughtnear a charged body, it acquiressome charge. This phenomenon of an uncharged body getting chargedmerely by the nearness of a chargedbody is known as induction. In Fig. 4.5, a positively-charged body A is broughtclose to a perfectly-insulated
uncharged body B. It is found that the end of B nearer to A gets negatively charged whereas further end becomes positively charged. The negative and positive charges of B are known as induced charges. The negative charge of B is called ‘bound’ charge because it must remain on B so long as positive charge of A remains there.However, the positivecharge on the farther end of B iscalled free charge. In Fig. 4.6, the body B has been earthed by a wire.The positive chargeflows to earth leaving negative charge behind.If next A is removed, then this negativecharge will also go to earth, leaving B uncharged. It is found that :
(i) a positive charge induces a negative charge and vice-versa. each of the induced charges is equal to the inducing charge.
(ii)
4.1. Electric Potential and Energy
We know that a body raised abovethe ground levelhas a certain amount of mechanical potential energy which, by definition, is given by the amount of work done in raising it to that height. If, for example, a body of 5 kg is raised against gravitythrough 10m, then the potential energyof the body is 5 ´ 10 = 50 m-kg. wt. = 50 ´9.8 = 490 joules. The body falls because there is attraction due to gravityand always proceedsfrom a place of higher potentialenergy to one of lower potential energy. So, wespeak of gravitational potential energy or briefly ‘poten- tial’ at different points in the earth’s gravitational field.
Now, consider an electric field. Imagine an isolated positive charge Q placed in air (Fig. 4.15). Like earth’s gravitational field, it has its own electrostatic field which theoretically extends upto infinity. If the chargeXis very far away from Q, say, at infinity, then force on it is practically zero. As X is brought nearer to Q, a force ofrepulsion acts on it (as similar charges repel each other),
Fig. 4.15 hence work or energy is required to bring it to a point like A in the electric field. Hence, when at point A, charge X has some amountof electric potential energy. Similarother points in the fieldwill also havesome potential energy. In the gravitational field, usually ‘sea level’ is chosen as the place of ‘zero’ potential. In electric field infinity is chosen as the theoretical place of ‘zero’ potential although,in practice, earth is chosen as ‘zero’potential, because earth is such a large conductor that its potentialremains practically constant although it keeps on losing and gaining electriccharge every day.
4.2. Potential and Potential Difference
As explained above, the force actingon a charge at infinityis zero, hence ‘infinity’ is chosen as the theoretical place of zero electric potential. Therefore, potential at any point in an electric field may be defined as
numerically equal to the work done in bringinga positive charge of one coulomb from infin- ity to that point against the electric field.
The unit of this potential will depend on the unit of charge taken and the work done.
If, in shifting one coulomb from infinity to a certainpoint in the electric field,the work done is one joule, then potential of that ponit is onevolt.
Obviously, potential is work per unit charge,
Similarly, potential difference (p.d.) of one volt exists betweentwo points if one joule of work is done in shifting a chargeof one coulomb from one point to the other.
4.1. Breakdown Voltage and Dielectric Strength
An insulator or dielectric is a substance within which thereare no mobile electrons necessary for electric conduction. However,when the voltageapplied to such an insulator exceeds a certainvalue, then it breaksdown and allowsa heavy electriccurrent (much largerthan the usualleakage current) to flow through it. If the insulator is a solid medium, it gets punctured or cracked.
The disruptive or breakdown voltage of an insulator is the minimumvoltage required to break it down.*
Dielectric strength of an insulator or dielectric medium is given by the maximum potential difference which a unit thickness of the medium can withstand without breaking down.
In other words, the dielectric strengthis given by the potential gradient necessary to cause break- down of an insulator. Its unit is volt/metre (V/m) although it is usually expressed in kV/mm.
For example, when we say that the dielectric strength of air is 3 kV/mm, then it means that the maximum p.d. which one mm thicknessof air can withstand across it withoutbreaking down is 3 kV or 3000 volts. If the p.d. exceeds this value, then air insulation breaks down allowing large electric current to pass through.
Dielectric strengthof various insulating materials is very important factor in the design of high- voltage generators, motors and transformers. Its value depends on the thickness of the insulator, temperature, moisture, content, shape and several other factors.
For example doubling the thickness of insulation does not doublethe safe workingvoltage in a machine.**
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* Flashover is the disruptive discharge which taken places over the surfaceof an insulator and occurswhen the air surrounding it breaks down. Disruptive conduction is luminous.
** The relation between the breakdown voltage V and the thickness of the dielectric is given approximately by the relation V = At2/3
where A is a constant depending on the nature of the medium and also on the thickness t. The above statement is known as Baur’s law.
| Table No. 4.1 Dielectric Constant and Strength (*indicates average value) | ||
| Insulating material | Dielectric constant or relative permittivity (er) | Dielectric Strength in kV/mm |
| Air | 1.0006 | 3.2 |
| Asbestos* | 2 | 2 |
| Bakelite | 5 | 15 |
| Epoxy | 3.3 | 20 |
| Glass | 5-12 | 12-100 |
| Marble* | 7 | 2 |
| Mica | 4-8 | 20-200 |
| Micanite | 4-5-6 | 25-35 |
| Mineral Oil | 2.2 | 10 |
| Mylar | 3 | 400 |
| Nylon | 4.1 | 16 |
| Paper | 1.8-2.6 | 18 |
| Paraffin wax | 1.7-2.3 | 30 |
| Polyethylene | 2.3 | 40 |
| Polyurethane | 3.6 | 35 |
| Porcelain | 5-6.7 | 15 |
| PVC | 3.7 | 50 |
| Quartz | 4.5-4.7 | 8 |
| Rubber | 2.5-4 | 12-20 |
| Teflon | 2 | 20 |
| Vacuum | 1 | infinity |
| Wood | 2.5-7 | --- |
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