Electric Charge Quantization Assignment Help

Electrostatics - Electric Charge Quantization

Electric Charge Quantization

QThe quantization of electric charge is the property by virtue of which all free charges are integral multiple of a basic unit of charge represented by thus charge q or body is always given by 
q = ne

Where n is any integer, positive or negative. The basic unit of charge is the charge that an electron or proton carries. By convention, charge on an electron is taken to be negative, therefore, charge on an electron is written as (-e) and charge on a proton is (+e).

The value of the basic unit of charge or elementary charge is,

e = 1.6 x 10-19 coulomb

It is one of the important constants of nature. If a body contains n1 electrons and n2 protons, the total amount of charge on the body is 

Q = n2 (e) + n1 (-e) = (n2 – n1e

As n1, n2 are integers their difference must also be an integer. Thus the charge on anybody is always an integral multiple of e and can be increased or decreased also in steps of e.

Thus any charged body or charged particle can possess charge equal to  ±1e,  ±2e, ±3e, and so on. The possible values of charge are,

Q = ± e = ± 1x 1.6 x 10-19 C

= 1. 6 x 10-19 C

Q = ± 2e = ± 2 x 1.6 x 10-19 C
= ± 3. 2 x 10 – 19 C

Q = ± 3e = ± 3 x 1.6 x 10-19 C
= ± 4. 8 x 10-19 C

And so on. The values of charge lying in between these values are not possible. 

The cause of quantization is that only integral number of electrons can be transferred from one body to another on rubbing. For example when one electron is transferred, the charges acquired by the two bodies will be q = ± 1e = ± 1.6 x 10-19 C. similarly when n electrons are transferred the charges acquired by the two bodies will be q = ± ne = ± n x 1.6 x 10-19 C.

The quantization of charge was first suggested by the experimental laws of electrolysis discovered by faraday. It was actually demonstrated experimentally by Millikan in 1912. Thus quantization of charge is an experimentally verified law in all domains of nature. Like charge; energy and angular momentum are also quantized.

Note quantization of charge is meaningful only at the microscopic level, where the charges involved are of the order of a few tens or hundreds of they can be counted. Such charges appear in discrete lumps and quantization of charge cannot be ignored. 

However at the macroscopic level we deal with charges of a few micro coulombs, a charge of magnitude 1 u C contains electrons whose number n = q / e = 1 x 10-6 C / 1. 6 x 10-19 C ≈ 1013, which is very large.

At this scale, the fact that charge can increase or decrease only in units of e is not visible. The grain nature of charge is lost and it appears to be continuous. The situation cane compared with the geometrical concepts of points and lines. A dotted line viewed from a distance appears continuous to us but is not continuous in reality. As many points very close to one another normally give an impression of a continuous line many small charges taken together appear as a continuous charge distribution. Hence at macroscopic level, quantization of charge has no practical consequence and it can be ignored. 

What is the value of charge on a body which carries 20 excess electrons?

Sol: here n = 20,

E = 1.6 x 10-19 C

As q = ne ∴ q = 20 (-1.6 x 10-19)

= - 3.2 x 10-18 C

2. Is a charge of 5.8 x10-18 C possible?

Sol: from q = ne

N = q/e = 5.8 x 10-18 / 1.6 x 10-19 = 36. 25

As n is not integer, this value of charge is not possible

Additively of charge 

This is a property by virtue of which total charge of a system is obtained simply by adding algebraically all the charges present anywhere on the system. It means charges ad up like real numbers 0, or charges are scalars like the mass of a body if a system contains n charges q1, q2, q3 ….qn then the total charge of the system is 

Q = q1 + q2 + q3 + … + qn

Charge has magnitude only but no direction, similar to the mass however mass of a body is always positive, but charge can be either positive or negative. Therefore, proper signs have tube used while adding the charges in a system. For example if a system contains charge + q – 2 q + 3 q and + 5 q then the total charge of the system is  = +q – 2q +3q +5q = + 7q

While taking sum of the charges, their signs (±) must be taken into account. 

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