Class 12 Electric Charges and Fields Notes

The NCERT textbook explains charge and its impacts on other charged objects in the presence of an electric field. Here are important points about charge.

• NCERT Definition: The Electric Charge is the intrinsic property of matter due to which it experiences a force when placed in an electromagnetic field.
• Types of Electric Charges: There are two types of electric charge: positive and negative. The positive Charge (+ve) is a result of the absence of free electrons in conductors. The negative charge (-ve) means the conductor or the object has excess electrons.
• The like charges repel each other and opposite charges attract each other; this property is called polarity of charges.

Properties of Electric Charges

• Electric charge follows the basic algebraic operations such as addition, subtraction, and multiplication. It is  considered a scalar quantity

•  The total charge in an isolated system is the algebraic sum of all charges in the system. Mathematically:

  $$Q_{\text{total}}=Q_1+Q_2+Q_3+\cdots +Q_n$$

• Electric charge always exists as an integral multiple of the quantum unit of charge (the charge of an electron). $$Q=n\cdot e$$
• Electric charge can be only transferred from one object to another, but charge can not be either created or destroyed. Also, the net charge for an isolated system remains constant.
• The velocity doesn't have any impact on the numerical value of charge, unlike mass, which changes with velocity.
• The electric charge always remains on the surface of the conductors. This happens due to the tendency of a system of charges to get a stable state by minimizing the total potential energy due to electrons present in the conductor.

Electric charges give rise to electromagnetic interactions, which are carried by subatomic particles like Protons and electrons. The concept of electric charge is central to electromagnetism which makes it important for CBSE board students.

Read in Detail:

Basic Properties of Electric Charge

What are Conductors?

Conductors are those materials that allow electric charge to flow freely through them. These materials have very little resistance to electric charge movement. JEE Main exam and NEET exam students must learn about these materials. Their lower resistivity makes conductors important for electrical circuits and systems. Some of the key characteristics of conductors are as follows:

• Conductors have high electrical conductivity, which measures the ability of a material to conduct an electric current.
• Most of the conductors are metals, including Copper, Aluminium, Gold and silver. 
• Outer electrons of atoms are loosely bound in the nucleus of metallic conductors.
• Electrons are free in a conductor, which allows the flow of electric current.
• The conductivity of most conductors decreases with an increase in temperature.

What are Insulators?

Insulators are those materials that resist the free flow of electric charge. These materials have very tightly bound electrons that cannot move freely through the material. Some of the key characteristics of insulators are:

• Insulators have very high electrical resistivity, which means they strongly resist the flow of electric charge.
• The electrons of the atoms in insulators are tightly bound to their nuclei, and they are not free to move around. 
• Insulating properties of some materials may change with temperature.
• Insulators are used in many places, including circuit boards, power lines, electrical wiring and electronic devices.

Read in Detail: Conductors and Insulators

The process of transferring electric charge to a body is called charging. There are three methods of charging;

• Charging by friction: The process of transferring free electrons from one object to another by rubbing them on each other is called charging by friction. The outermost shell breaks free and transfers to another body when it gets enough external energy due to friction.

• Charging by conduction: The process of transferring free electrons through contact (an uncharged object touches any charged object). In this method, objects must be conductors.

• Charging by induction: The method of charging an uncharged conductor due to its property of repulsion from like charges and attraction with unlike charges. In this method, when an uncharged body is only near but not in touch causes electrons to displace due to repulsion. when connected with earthing one side will become neutral and other will be charged.

Coulomb’s law describes the electrostatic force between two point charges. As per the law, the force between two point charges is directly proportional to the product of the magnitudes of electric charges and inversely proportional to the square of the distance between them. Many questions based on this law will be asked in the IIT JAM exam and the IISER entrance exam. 

$F = k_e \frac{ \left| q_1 q_2 \right| }{r^2}$

Here:

• F is the magnitude of the electrostatic force between charges $q_1 \text{ and } q_2$ are magnitudes of two point charges

• r is the distance between two charges
• $k_e$ is called as Coulomb's constant

The force between multiple electric charges can be determined through the principle of superposition in addition to Coulomb's law. The principle of superposition states that total force that acts on a charge because of other charges is the vector sum of individual forces that are exerted by other charges. Let us say there is a system of three charges $q_1,q_{2}and{q}_3$ . The force on one charge because of the other two charges can be obtained by performing a vector addition of the force due to each one of these charges. Therefore, if force $q_1$ on due to $q_2$ is denoted by ${\mathbf{F}}_{ 1 2 } , {\mathbf{F}}_{ 1 2 }$ will be as the below equation even when the charges are present.

$F_1=F_{12}+F_{13}+\dots +F_{\mathrm{1n}}=\frac{1}{4\pi {\epsilon }_0}[\frac{q_1{q}_2}{{r_{12}}^2}\widehat{r_{12}}+\frac{q_1{q}_3}{{r_{13}}^2}\widehat{r_{13}}+\dots +\frac{q_1{q}_n}{{r_{\mathrm{1n}}}^2}\widehat{r_{\mathrm{1n}}}]$

=  $\frac{q_1}{4\pi {\epsilon }_0}\underset{i=2}{\sum }{n}^{}\frac{q_i}{{r_{1i}}^2}\widehat{r_{1i}}$

Read in Detail: Forces between Multiple Charges

In reality, electric charge does not exist in discrete packets. Rather, we need to work with continuous charge distributions. How to calculate the total or net charge in a continuous charge distribution, let's learn.

There are three types of continuous charge distribution:

• Linear Charge Distribution\

The charge is continuously distributed along a one-dimensional line such as a charged wire or thin rod

Linear Charge density (λ):

$$\lambda =\frac{dq}{dl}\left(\text{units: C/m}\right)$$

where $dq$is the charge on a small length $dl$.

• Surface Charge Distribution

The charge is distributed over a two-dimensional surface, such as a charged sheet or the surface of a charged conductor

Surface charge density (σ):

$$\sigma =\frac{dq}{dA}\left({\text{units: C/m}}^2\right)$$

where $dq$is the charge on a small surface element $dA$

• Volume Charge Distribution

The charge is distributed throughout a three-dimensional volume, such as a charge distributed inside a charged sphere or volume of material.

Volume charge density (ρ):

$$\rho =\frac{dq}{dV}\left({\text{units: C/m}}^3\right)$$

where $dq$ is the charge in a small volume element $dV$.

Summary of continuous charge distribution

Charge Distribution Type	Charge Density Symbol	Formula for Total Charge
Linear	$\lambda$	$Q = \int \lambda \, dl$
Surface	$\sigma$	$Q = \int \sigma \, dA$
Volume	$\rho$	$Q = \int \rho \, dV$

Read in Detail: Continuous Charge Distribution

 

An electric field describes the influence of a charge on space around it. It has a vector field with both magnitude and direction at each point in the space. Electric field at a particular point is defined as the force per unit charge that positive charge will experience when placed at that point. 

Mathematically, the electric field E at a point in space is given by force F which is experienced by a positive test charge q placed at that point, divided by the magnitude of the test charge.  

$\mathbf{E} = \frac{\mathbf{F}}{q}$