Tutorial Course

# 12th Standard - Physics Tutorial - NCERT - CBSE Pattern

We will cover below chapters.
• ELECTRIC CHARGES AND FIELDS
• ELECTROSTATIC POTENTIAL AND CAPACITANCE
• CURRENT ELECTRICITY
• MOVING CHARGES AND MAGNETISM
• MAGNETISM AND MATTER
• ELECTROMAGNETIC INDUCTION
• ALTERNATING CURRENT
• ELECTROMAGNETIC WAVES
• RAY OPTICS AND OPTICAL INSTRUMENTS
• WAVE OPTICS
• DUAL NATURE OF RADIATION AND MATTER
• ATOMS
• NUCLEI
• SEMICONDUCTOR ELECTRONICS: MATERIALS, DEVICES AND SIMPLE CIRCUITS

# ELECTRIC CHARGES AND FIELDS

## 1.2 Electric Charge

Electric charge a property of a matter due to which it experiences and produces electric and magnetic field. Types of charges
• positive charge - Electron deficiency
• negative charge - Excess Electron

## 1.4 Basic Properties of Electric Charge

• Charge is a scalar quantity
• Charge is transferrable
• Charge is alway associated with mass
• Charge produces electric and magnetic field
• Like charges repel each other. Unlike charges attract each other
• Charge is conserved - Charge can neither be created nor destroyed!
Charge on 1 electron is $-1.6 \times 10^{ -19}C$
Charge on 1 proton is $+1.6 \times 10^{ -19}C$
Charge on 1 neutron is 0.
Mass of 1 electron is $m_e = 9.1 \times 10^{ -31}kg$
Mass of 1 proton is $m_p = 1.67 \times 10^{ -27}kg$
Mass of 1 neutron is $m_n = 1.68 \times 10^{ -27}kg$

is $+1.6 \times 10^{ -21}C$ charge possible? and answer is No because$+1.6 \times 10^{ -21}C$ is equal to $\frac{+1.6 \times 10^{ -19}} {100}C$. We can not have a charge that is a fraction of Electron!

## 1.5 Coulomb's Law

There is a force between 2 charges which can be calculated using below formula! It is also called as Coulomb's law!
$F = k \cdot \frac {q1 \cdot q2} {r^2}$
Here k is Coulomb Constant and it's value is $\frac{1}{4 \pi \epsilon_0}$. Epsilon 0 is a permittivity of free space and it's value is $8.854 \times 10^{-12} \text{ } C^{2} N^{-1} m^{-2}$.This law is valid only for point charges!

## 1.6 Forces between Multiple Charges

Force is a vector!
Properties of forces
• Force is conservative
• Force is central
• Force follows inverse square law
• Force depens on medium unlike gravitational force!
• It is infinite ranged force

### Superposition of Forces

When multiple charges interact with each other, you will need to take the vector sum of all forces!

### Relative permittivity

Ratio of permittivity of medium and permittivity of vaccum! If F is a force between 2 charges in vaccum, then force between same charges in medium of relative permittivity$(\epsilon_r)$ is $\frac{F} {\epsilon_r}$

## 1.7 Electric Field

Electric field of a charged particle is an invisible region surrounding the charged particle in which it can exert an electrical force on another charged particle! There can be other charged particles inside the electric field. So 2 electric fields can overlap and electric lines of force can superpose! Electric field intensity is the amount of force experienced by unit charged particles when it is placed in the electric field.
$E(r) = \frac{F(r)} {q}$
$F(r) = E(r) \cdot q$

Electric field intensity due to different charges distribution
• Point charge
• Line charge
• Ring Charge
• Hollow Sphere
• Solid Sphere
• Sheet Charge
• Dipole (axial and equitorial) - System of 2 equal and opposite charges seperated by a small fixed distance is called as dipole!

### Point Charge

Electric Intensity of a point (Force experience by the point in field) in a Electric field generated by a Point Charge (q) can be calculated using below formula.
$E = k \cdot \frac {q} {r^{2}}$

### Line charge

To find the electric field intensity (E) at a point in the electric field generated by a linear charge density (lambda) along a straight line, you can use the following formula:
$\frac{2k\lambda}{r}$
Where:
- E is the electric field intensity at the point (measured in volts per meter, V/m).
- k is Coulomb's constant.
- lambda is the linear charge density, which is the charge per unit length along the line (measured in coulombs per meter, C/m).
- r is the distance from the line charge to the point where you want to find the electric field intensity (measured in meters, m).
This formula is applicable when you want to calculate the electric field intensity at a point due to a linear charge distribution along a straight line. It describes how the electric field intensity decreases with distance (r) from the line charge.

### Ring Charge

To find the electric field intensity (E) at a point on the axis of a uniformly charged ring with total charge Q, you can use the following formula:
$E = \frac{kQx}{(x^2 + R^2)^{3/2}}$
Where: - E is the electric field intensity at the point on the axis (measured in volts per meter, V/m). - k is Coulomb's constant - Q is the total charge of the ring (measured in coulombs, C). - x is the distance along the axis from the center of the ring to the point where you want to find the electric field intensity (measured in meters, m). - R is the radius of the ring (measured in meters, m). This formula is applicable when you want to calculate the electric field intensity at a point on the axis of a uniformly charged ring due to the presence of the ring charge. It describes how the electric field intensity varies with distance (x) from the center of the ring.

### Dipole

#### Dipole in External field

Uniform external field, Non Uniform external field You can watch https://www.youtube.com/watch?v=MVvHdH6n2VE by Anupam Sir from Vedantu for more details!

## 1.8 Electric Field Lines

Electric field lines are imaginary lines of electric forces through a region of empty space so that tangent at any point on the line is in the direction of the electric field vector at that point. Electric field lines emerge from positive charge and terminate at negative charge if negative charge exists!

## 1.9 Electric Flux

Electric flux is the measure of Electric Field through a given surface. Formula to find the Electric flux is given below.
$\phi = E \cdot A$
It is assumed that Electric field (E) is constant and A is a surface area through which flux is to be measured!

## 1.13 Gauss's Law

Gauss's Law states that flux of a charge enclosed inside a body is given by below formula.
$\phi =\frac {q} {\epsilon_0}$

# ELECTROSTATIC POTENTIAL AND CAPACITANCE

## 2.1 Introduction

Electric charge has intensity and potential! Potential Energy is the negative work done by conservative force! Work done by external force is equal to negative work done by conservative force!

# ATOMS

## 12.1 Introduction

Thomson Model of Atom says that it is like a watermelon and seeds are like electron and red part is proton. But this model could not explain spectral series of Hydrogen Atom and also could not explain the observations in gold foil scattering experiment!

## 12.2 Alpha-particle Scattering and Rutherford's Nuclear Model of Atom

Gold foil was bombarded with alpha particles from Bismuth (Radioactive Source). Alpha particle has 2 proton and 2 electron!
Observations in Gold foil experiment
• Most of the Alpha particles went undeflected within 1 degree
• Only 0.14% Alpha particles delected more than 1 degree
• Nearly 1 in 8000 deflected by more than 90 degree
• Hardly any particle returned by 180 degree
Conclusions in Gold foil Alpha Scatteing experiment
• Most of the Alpha particles went straight that means most of the atom space is empty
• Large angle deflection happened due to the positive charge at nucleus
• Nucleus is surrounded by Electrons
• 180 degree relection happened and reason is that When Alpha particle reaches the nuclues, it's kinetic energy gets converted into Potential Energy and due to electrostatic repulsive force, it gets deflected by 180 degree. The Smallest distance upto which alpha particle can reach is called as the distance of closet approach!
Alpha particle trajectory path depends on impact parameter! Lesser Impact parameter means larger scattering. Head on collision means maximum scattering!
Rutherford atomic model limitations
• This model does not explain why electron is not losing energy and collapsing into nucleus.
• Why hydrogen is emitting discrete line spectrum

## 12.4 Bohr Model of the Hydrogen Atom

• Centripetal force is provided by Electrostatic Force
• Quantum Condition
• Stationary Orbits
• Frequency Condition
Finding the velocity of electron and radius of hydrogen orbits
Finding the energy of Hydrogen electron revolving in the orbit!

## 12.5 The Line Spectra of the Hydrogen Atom

series obtained due to transitions!