Electric charge and field Oneshot in 30 minutes | Class 12th Physics Chapter 1 Oneshot CBSE JEE NEET

Name: Electric charge and field Oneshot in 30 minutes | Class 12th Physics Chapter 1 Oneshot CBSE JEE NEET
Uploaded: 2023-02-15T16:16:00.000Z
Duration: 1 h 53 s

Introduction to Electric Charge

Overview of the Chapter

The video introduces the topic of electric charge, indicating it will cover important points from the first chapter of Class 12 Physics in a quick revision format.

Viewers are encouraged to join a Telegram channel for access to notes and discussions with over 70 students.

Definition and Types of Electric Charge

Electric charge is defined as a property of materials that allows them to exert electrostatic forces on other materials, either attracting or repelling them.

There are two types of charges: negative and positive. A body gains a negative charge by acquiring extra electrons, while it becomes positively charged when it loses electrons.

Properties and Behavior of Charged Bodies

Mass Changes Due to Charging

When an electron leaves a positively charged body, its mass decreases; conversely, when an electron enters a negatively charged body, its mass increases due to the added mass of the electron.

Charge Quantities

The charge on an electron is approximately -1.6 x 10^-19 coulombs, while protons have an equal but positive charge. Neutrons carry no charge.

Methods of Charging Objects

Charging Methods Explained

Three methods for charging objects include:

Charging by Friction: Rubbing two bodies transfers electrons from one to another.

Charging by Conduction: Involves direct contact between charged and uncharged bodies.

Charging by Induction: Charges without direct contact; involves bringing a charged object close enough to influence another object's charges.

Detailed Explanation of Charging Methods

Examples and Mechanisms

In charging by conduction, touching a positively charged rod causes electrons to move into the metal sphere, resulting in a net positive charge on the sphere.

In induction, bringing a positively charged rod near an uncharged object attracts electrons towards it without physical contact. Grounding can neutralize excess positive charge.

Fundamental Properties of Charge

Key Principles Discussed

Four fundamental properties include:

Relativity of Charge: Charges can be added algebraically regardless of their direction.

Conservation of Charge: Total electric charge remains constant in isolated systems.

Quantization of Charge: Charges exist in discrete packets (quanta).

Additivity of Charge: Net charge is determined through algebraic addition.

Understanding Charge Quantization and Coulomb's Law

Charge Quantization

Charge is transferred in fixed quantities, meaning a body becomes charged only when electrons are transferred. This principle is known as the quantization of charge.

The transfer of charge occurs in integral multiples of the electron's charge, indicating that one, two, or more electrons can be transferred at once.

The total charge on a body will always be an integer multiple of the elementary charge (the charge of a single electron), which can be positive or negative.

Coulomb's Law

Coulomb's law describes the force between two charges, given by the formula F = q_1 q_2/r^2 , where r is the distance between charges.

The constant k = 1/4piepsilon_0 relates to the permittivity of free space and helps define units for force in Newton-meters squared.

Vector Formulation

When expressing forces as vectors, direction must be included. For example, F_12 indicates the force on charge 1 due to charge 2.

The vector form requires understanding that forces act in opposite directions; thus, if q_1 experiences a force from q_2 , then q_2 's force on q_1 is equal and opposite.

Electric Field Concept

The electric field constant explains how different mediums affect forces between charges. It compares forces in vacuum versus other media.

The ratio of these forces gives us the dielectric constant, which does not have units but indicates how much weaker a force becomes in a medium compared to vacuum.

Electric Field Lines

Electric field lines are imaginary lines representing how charges exert forces on each other. They illustrate directionality: outward for positive charges and inward for negative ones.

Understanding Electric Fields and Dipoles

Electric Field Direction and Properties

The discussion begins with the concept of electric fields, emphasizing that they move from positive to negative charges. A tangent drawn at any point indicates the direction of force on a positive charge.

Electric field lines are imaginary lines that help visualize the direction of force acting on a charge placed at a specific point. For similar charges, these lines create neutral points where the electric field is zero.

Electric field lines start from positive charges and end at negative ones, forming smooth curves rather than closed loops. This characteristic highlights their continuous nature.

On metal surfaces, electric field lines are perpendicular to the surface. Two electric field lines never intersect; if they did, it would imply two different directions of force at one point, which is impossible.

Force on Charges in an Electric Field

Any charge placed in an electric field experiences a force. The formula for calculating this force is F = k cdot q_0 , where q_0 represents the test charge experiencing the force.

The relationship between electric field (E), force (F), and test charge (q0) can be expressed as E = F/q_0 . Here, q_0 is typically very small to avoid influencing the field itself.

Understanding Dipoles

A dipole consists of equal and opposite charges separated by a distance denoted as 2a. There are three key points associated with dipoles: axial points along the axis, equatorial points perpendicular to it, and general points elsewhere.

The strength of a dipole is described by its dipole moment (p), calculated using either charge's magnitude multiplied by the distance between them. The direction of this vector quantity goes from negative to positive charge.

Calculating Electric Fields Due to Point Charges

For a single point charge, the formula for calculating its electric field at a certain distance r is given by E = k/q^2 .

When considering an axial point due to a dipole, its electric field can be calculated using E = k(2p)/r^3 . In contrast, for equatorial points, it’s given by E = k(p)/r^3 .

Key Comparisons Between Axial and Equatorial Points

The electric field strength at an axial point is twice that at an equatorial point due to differences in their respective formulas.

Electric Flux and Gauss's Law

Understanding Electric Flux

The concept of electric flux is introduced, defined as the number of electric field lines passing perpendicularly through a surface.

Electric flux depends on two factors: the intensity of the electric field and the area of the surface. If there is an angle between the electric field lines and the area vector, cosine theta (cos θ) is used in calculations.

It’s clarified that theta refers to the angle between the electric field vector and area vector, not between two electric fields or areas.

The relationship between dot products and scalar quantities is emphasized; when calculating flux, cos θ comes into play due to its scalar nature.

The notation for small surfaces involves using differential elements (dS), indicating integration over smaller areas to find total flux.

Gauss's Law

Gauss's Law states that for any closed body containing charge, the total electric flux through that surface equals fracQ_encepsilon_0 , where Q_enc is enclosed charge.

This law applies only to closed surfaces; if not closed, Gaussian surfaces must be considered for symmetry in calculations.

The proof of Gauss's Law involves integrating over a closed surface where angles are zero degrees between vectors involved in calculations.

An example involving a charged wire illustrates how to apply Gauss's Law by enclosing it within a cylindrical Gaussian surface to derive its electric field at infinity.

Applications of Gauss's Law

When applying Gauss’s Law to long charged wires, it’s crucial that they remain enclosed within a symmetrical shape like a cylinder for accurate results.

Integration across curved surfaces shows how angles affect calculations; zero-degree angles yield straightforward integrations while 90-degree angles complicate them.

The formula derived from integrating over cylindrical surfaces leads to expressions involving linear charge density ( lambda ) and distance from the wire ( r ).

Electric Field from Charged Sheets

For charged sheets, similar principles apply; however, one must consider both sides' contributions when calculating net electric fields due to their planar symmetry.

Angles formed with respect to flat surfaces are critical—90 degrees on one side leads to different considerations than those at zero degrees on another side during integration.

Understanding Electric Fields and Charge Distributions

Electric Field from Charged Sheets

The electric field generated by a charged sheet on one side is represented as sigma divided by two epsilon naught. This concept is crucial for understanding the behavior of electric fields around charged sheets.

When dealing with similar charged sheets, three regions are identified: one near each charge and one in between. The electric fields in these regions interact based on their directions.

In cases where both sheets have similar charges, the net electric field in the middle region becomes zero due to opposing directions of the fields from each sheet.

Behavior of Electric Fields with Different Charges

For oppositely charged plates, while the sides exhibit an electric field, the middle region's field can be calculated as sigma divided by epsilon naught.

Understanding how electric fields behave at various points around conductive spheres is essential; outside a conducting sphere, it behaves as if all charge were concentrated at its center.

Calculating Electric Fields

The formula for calculating the electric field outside a conducting sphere involves using surface charge density (sigma), area (A), and constants like 4πepsilon naught.

Inside a conducting sphere, the electric field is zero because there’s no charge present within that space; all charge resides on the surface.

Electric Field from Rings and Dipoles

To calculate the electric field along an axis of a charged ring, specific formulas involving distance and charge must be applied effectively.

When dipoles are placed in an electric field, they experience torque due to forces acting on positive and negative charges differently.

Torque in Dipoles

The torque experienced by dipoles can be calculated using forces acting on them and their perpendicular distances from pivot points.

Two types of equilibrium exist for dipoles: stable equilibrium occurs when angles between dipole moment and electric field are zero degrees; unstable equilibrium occurs at 180 degrees.

In stable equilibrium, if disturbed, a dipole returns to its original position; however, in unstable equilibrium, it does not return once displaced.