# Basic Properties of Electric Charge for JEE Main

## Electric Charge - Properties and Solved Examples

In a general terminology, electric charge is the amount of energy or electrons that pass from one system to another system. This transfer can be mediated by different mechanism such as conduction, induction, or other specific methods. Electric charges are divided in two categories namely positive (+) charge, and negative charges (-). Charges are present in almost every system. However, several systems do not have charges, either have no charge or have neutral charge. Protons, electrons, and neutrons are the example of the basic subatomic particles, in which proton possesses positive electrical charge, electron possesses negative electric charge and neutron has neutral charge. The symbol of charge is ‘q’ or ‘Q’. The total charge of electrons present in an atom is the number of electrons multiplied by the charge of an electron. According to this definition, the formula for charge can be written as,

Q = ne,

Where Q is a charge, e is charge on one electron, and n is number of electrons. It is possible to measure the charge of a body by comparing it to a standard value. According to a study, the charge of electron is 1.6 x 10-19C. The S.I. unit or Standard unit of electric charge is Coulomb and it is denoted by ‘C’.

Definition of 1 C:

If the current flowing through the wire is 1 A, then 1 C can be defined as the charge flowing or passing through a wire in 1 second.

There are very two basic properties of electric charge. They are:
• • Similar electric charges tend to repel each other.

• • Opposite electric charges tend to attract each other.

• For example, two protons, and two electrons repel each other. In case of proton and electron, they tend to attract each other. These properties depend on the nature of charge i.e. the force acting on them and coordinating the direction of flow. The proton and electron possess the same amount of charge but they are opposite in nature. (Note: The charge of proton is 1.6 x 10-19 C, where as the charge of electron is -1.6 x 10-19 C.) The difference is the type of charge they carry.

Basic Properties of Electric Charge

There are certain basic properties of electric charge that they follow. The electric charges are considered as point charges if the size of the electrically charged bodies is so small. Apart from the above-mentioned properties of electric charge, there are certain other basic properties they possess. They are:

• 1. Additive property of electric charge

• 2. Conservative nature of charge

• 3. Quantization of charge

• In this section, these properties are described in details.

• 1. Additive property of electric charge

• Electric charges are additive in nature, and it depends upon the type of electric charge they carry. It is a scalar property. It is possible to add them directly. For example, let us consider a system containing only two charges, namely q1 and q2. According to this property, the total charge of the system can be calculated by algebraic sum of q1 and q2 i.e. q1 + q2. Similarly, the same thing holds if there are more than two electric charge particles. Suppose, a system contains q1, q2, q3, q………. qn, then the net charge of the whole system can be calculated by summation.
Net Charge = q1 + q2 + q3 + q4 + ……. + qn

• 2. Conservative nature of electric charge

• Electric charge of a particle is conservative in nature. It means that the charge can neither be created nor be destroyed. The charges can be transferred from one system to another system by the mechanism like conduction, and induction. It is similar to the law of conservation of mass and also, similar to the first law of thermodynamics (i.e. law of conservation of energy). Rubbing of two bodies involves a transfer of electrons from one body to another.

As for example, let us consider a system containing a total of 10C charge. It is possible to redistribute that charge as 2C, 3C, and 5C or it is also possible to redistribute it according to any other possible permutation. Sometimes several systems tend to lose equal number of protons and electrons. Hence, the final charge of the system would be having exactly similar charge as it was present initially. This condition is seen in neutrino decay. During the decay, neutrino lose one electron and one proton. Ultimately, the total charge of the system will be zero as it loses electrons and protons of the same magnitude and opposite signs.

• 3. Quantization of Charge

• The charge of a system is a fixed quantity. Technically, the charge is a quantized quantity. The net charge of a system can be expressed as the integral multiples of the basic unit of charge (i.e. 1.6 x 10-19 C. Suppose, the net charge of the body is q, then it can be written as:
q = ne
In this formula, n represents an integer number and it can not be fractional or irrational number. So, the value of n can be any positive or negative integer. For example, value of n can be 1, -1, 2, -3, 4, -5 etc. The symbol ‘e’ represents the basic unit of the charge that is carried by electron and/or proton. Conventionally, the charge on proton is simply denoted as ‘e’, while the charge on electron is denoted as ‘-e’.

The principle of the quantization of electric charge was first proposed by English scientist Faraday. This proposal was based on his experimental laws of electrolysis, and in 1912, this principle was demonstrated and proved by Millikan.

It was reported that 1 A Coulomb of charge has around 6 x 1018 number of electrons. In general, particles do not have a high magnitude of charge, and hence, the smaller units of coulomb are generally used in routine practice. Commonly used units for electric charge are micro-coulomb or milli-coulomb.

Micro coulomb can be denoted as ‘μC’ and milli coulomb is denoted as ‘mC’. The conversion factor from milli coulomb to coulomb is:

1 mC = 10-3 C
Similarly, the conversion factor from micro coulomb to coulomb is:
1 μC = 10-6 C

The concept of quantization of electric charge is very important to calculate the total amount of electric charge present in a system by using equation ‘q = ne’. Suppose, for example, a system has total n1 number of electrons and total n2 number of protons. Then, based on these properties, we can say that the total amount of charge can be represented as n2 e – n1 e.

Net amount of charge = n2 e – n1 e

OR

Net amount of charge = (n2 – n1) e

Solved Example Using Above-mentioned Properties

Problem 1
: A system is made up of 6 subatomic particles, in which there are 4 protons, and 2 electrons. The charge present on these six particles are + 2C, + 4C, + 10C, + 6C, - 4C, and – 2C. Calculate the net charge present within the system.
Solution:

According to the addition of property of electric charge, the net charge of a system is an algebraic sum of a charge of an individual subatomic particle.

Consider the total charge or net charge of system as ‘Q’. Then, according to the addition of property of electric charge,
Total charge of the system Q = 2 C + 4 C + 10 C + 6 C + (- 4 C) + (- 2 C)

Q = 16 C

Hence, the net charge of the system would be 16 C.

Problem 2: A system is made up of 10 subatomic particles, in which there are 4 protons, and 2 electrons and 4 neutrons. The charge present on these six particles are + 2C, + 4C, + 10C, + 6C, - 4C, and – 2C. Calculate the net charge present within the system.

Solution:

As we know, the charge present on one proton is e and the charge present on one electron is -e, as well as, the charge present on neutron is zero and it does not depend on the number of neutrons present in the system.
According to the addition of property of electric charge, the net charge of a system is an algebraic sum of a charge of an individual subatomic particle.

Consider the total charge or net charge of system as ‘Q’. Then, according to the addition of property of electric charge,
Total charge of the system Q = 2 C + 4 C + 10 C + 6 C + (- 4 C) + (- 2 C) + 0 + 0 + 0 + 0
Q = 16 C

Hence, the net charge of the system would be 16 C.

Thus, we can state that:

• 1. Electric charge is the amount of energy or electrons that pass from one system to another system.

• 2. Electric charges are divided in two categories namely positive (+) charge, and negative charges (-).

• 3. Charge is a scalar quantity. It has a specific magnitude and no direction.

• 4. Charge is a conserved quantity.

• 5. Similar charges repel, while opposite charges attracts each other.