Electric Charge

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electric field.

• Responsible for all electrical and electromagnetic phenomena.
• Denoted by the symbol Q

Electric charge is a scalar quantity, meaning it has magnitude only and no direction. Unlike vector quantities, it does not follow the triangle law of vector addition. Charges can be added algebraically, so the total charge is simply the sum of individual charges. Similarly, when electric currents meet at a junction, the resulting current is the algebraic sum of the currents.

Units of Electric Charge

The SI unit of Charge is Coulomb (C) and It is defined as "The amount of charge transferred by a current of one ampere in one second."

Other Units of Charge are

1. Faraday (where 1F = 94,485 Coulombs)
2. Ampere-hour (where 1 A-h = 3600 Coulombs)

Formula Of Electric Charge

For Continuous Flow

\boxed {Q= I \times t}

where,

• Q = electric charge
• I = electric current
• t = time

For Discrete Quantities

\boxed{Q=n \times e}

where,

• Q = charge passing through the conductor
• n = number of electrons
• e = charge on 1 electron (=1.6 × 10^-19 C)

Dimensional Formula of Electric Charge

As Electric Charge = Current × Time, Therefore Dimensional Formula of Electric Charge is [M⁰L⁰T¹I¹] ⇒ [T¹I¹]

Elementary of Electric Charge

(1 amu ≈ 1.66 × 10⁻²⁷ kg)

Condition for Electric Charge

Methods of Charging

Electric charge is a basic property of anything; it can be transferred from one body to another. The process of gaining or losing electric charge is called Charging.

Charging can be achieved in the following three ways:

1. Charging by Friction

When two things are rubbed together, electrons are transferred between them, and they become charged. Also, when a rubber balloon is rubbed with animal fur, the rubber balloon attracts the electrons from the animal fur. As a consequence, rubber has an abundance of electrons, whereas fur has a scarcity of electrons. These are known as charged objects. 

2. Charging by Conduction

The method of charging an uncharged object by bringing it close to a charged object is known as charging by conduction. The charged conductor has an unequal number of protons and electrons; hence, when an uncharged conductor is brought near it, it discharges electrons to stabilize itself.

3. Charging by Induction

The process of charging an uncharged conductor by bringing it near a charged conductor without any physical contact is known as charging by induction.

Basic Properties of Electric Charge

A charge is the fundamental property of an atom. It has various properties; some of the basic properties of electric charge are

• Force between two Charges
• Charges are additive in nature
• Quantisation of Charge
• Conservation of Electric Charge

1. Force between two Charges

There is a force between two charges, and its value is determined using Coulomb's law. The basic property of the charge is that

• Like Charges repel each other.
• Unlike Charges attract each other.

The following image shows the nature of the force between two charges.

2. Charges are Additive in Nature

Electric charge behaves as a scalar quantity and can be directly added to obtain a higher charge. For example, if we have three charges, q₁, q2, and q3, arranged in the system, then the total charge of the system is given by finding the algebraic sum of q₁, q2, and q₃.

Let’s take a system of n charges q₁, q₂, q₃, q₄, … …. q_n, then the net charge of the entire system (say Q) is calculated as,

Q = q₁ + q₂ + q₃ + q₄ + ……. + q_n

3. Quantisation of Charge

Quantization of the charge is the fundamental concept of physics. It signifies that a charge can neither be created nor destroyed and can only be transferred from one body to another. 

Also, the charge can exist as an integral multiple of the fundamental charge, i.e., Q = ne, which means charges of 2e, 4e, 98e, and others exist, but charges in the form of 1/2e, 3/4e do not exist.

4. Conservation of Electric Charge

Conservation of Electric charge states that "the total electric charge in an isolated system is always constant." We can also state that the net quantity of the electric charge (positive charge - negative charge) is always conserved.

Solved Problems

Problem 1: A current of 3 A flows through a conductor for 5 minutes. Find the total charge transferred.

Solution: t = 5 min = 300 s

Q = 3 × 300 = 900 C

Problem 2: How many electrons pass through a conductor if the charge transferred is 1 C?

Solution: n = \frac{Q}{e} = \frac{1}{1.6 \times 10^{-19}}

n=6.25×10¹⁸ electrons.

Problem 3: An atom has 15 protons and 18 electrons. Determine its charge.

Solution:

• Excess electrons = 18 − 15 = 3
• Charge = −3e

Q = −3 × 1.6 × 10⁻¹⁹ = −4.8 × 10⁻¹⁹ C

Problem 4: Two charges of 2 μC and 3 μC are placed 2 m apart. Find the force between them.

Solution: F = k \frac{q_1 q_2}{r^2}

F = 9 \times 10^9 \times \frac{(2 \times 10^{-6})(3 \times 10^{-6})}{(2)^2}

F = 9 \times 10^9 \times \frac{6 \times 10^{-12}}{4}

F = 13.5 \times 10^{-3} = 0.0135 \text{ N} \, \, (Repulsive)

Unsolved Problems

Problem 1: A current of 0.5 A flows for 10 minutes. Find the charge transferred.

Problem 2: Find the number of electrons required to produce a charge of 8 C.

Problem 3: Three charges (+2C), (-5C), and (+1C) are placed in a system. Find the net charge.

Problem 4: Two charges of (1 \mu C) each are placed 1 m apart. Find the force between them.

Problem 5: Is a charge of (4.8 \times 10^{-19}) C possible? Justify your answer.

Related Articles:

• Electric Field
• Electric Current
• Electric Field Lines
• Electric Potential Energy
• Coulomb's Law