Assignment Module 01 No. CE 01 Vector Mechanics of Particles

Transformation of Scalars and Vectors under Rotation Transformation

Q.1. Explain “Transformation of Scalars under Rotation Transformation” .

Q.2. Explain “Transformation of Vectors under Rotation Transformation” .

Q.3. Explain “Transformation of Scalars and Vectors under Rotation Transformation” .

Q.4. If a vector of magnitude A is rotated through certain degree, then what is the change in that    
        vector? 

 forces in nature

 
Q.5. Explain forces in nature.
Q.6. Explain about the basic forces in nature with its range and magnitude.

Form Invariance of Newton’s Second Law

Q.7. What do you mean by form Invariance of Newton’s second law, Explain. 

Q.8. Define Galelian Transformations. Derive the Transformation Equations.

Friction

Q.9.Define the term friction ? Explain types of friction.

Q.10. write the differences between static friction and dynamic friction.

Q.11. State the laws of friction.

Q.12. Explain the term angle of friction.

Q.13. Define coefficient of friction and limiting friction.

Newton’s equations of motion in Cartesian Coordinates

 Q.14. The position of a particle of mass m under the influence of a free particle is given by  

             Find the expression for its momentum.                                                   (AKU 2020)

 Q.14.The transformation matrix to move from a set of coordinates axes to a new set x¢, y¢, z¢ through   
         an angle q is 

       

Q.15. If a position vector is represented in a set of x,y,z co-ordinate

         system and x,y co-ordinate is rotated through angle 45° about z-axis. Find the
         transformed value of the components of the position vector A in new co-ordinate
         system of x¢, y¢,z¢.

 

 

Assignment Module 01 No. CE 02 Vector Mechanics of Particles

Question.1     Define vector field, Give two examples of each.

Question.2     Define del operator.

Question.3     What do you mean by gradient of scalar field?

Question.4     Define the divergence of a vector field.

Question.5     Define the curl of vector field.

Question.6     What do you meant by Solenoidal vector field?

Question.7     What do you meant by irrotational vector field?

Question.8     Define field. State two types of field.

Question.9     Under what conditions the vector field is solenoidal and irrotational?.

Question.10   State the physical meaning of grad f.

Question.11   State the values of position vector r and r.

Question.12   State the three fundamental operations with ∇ which are of physical interest.

Question.13   Define rotational vector Field.

Question.14   What do you meant by directional derivative.

 

Fermi function or Fermi dirac didtribution funtion

 

Fermi function or Fermi Dirac distribution function

The probability that a particular quantum state of energy E of fermions is occupied at a particular temperature T is given by a function f (E) and is called Fermi function. 

Let a system of electrons is in thermal equilibrium at a temperature T kelvin. 

The probability f(E) of an electron occupying a particular energy level E is given by

 

 

Where f (E) is Fermi function

E_F is called Fermi energy

K is Boltzmann constant
K = 1.38 × 10 ⁻²³ J/K

Value of Boltzmann constant in eV  is K = 8.62 × 10 ⁻⁵ eV/K

T is absolute temperature

For a filled energy level f (E) = 1

For an unfilled energy level f (E) = 0

Fermi function is obeyed by Fermions

Fermions are half integer spin particles.  Example : electrons which obey Pauli’s Exclusion principle.

Application of Fermi function or Fermi Dirac distribution function

 

 

Important Formula

 

Questions

1. what is fermi funtion or fermi dirac distribution function ?
2. What is Fermi level?
3. What is Fermi energy?  
4. Define Fermi velocity.
   
5. Explain thermal equilibrium in in semiconductors.
6. write the equation for the Fermi level energy in n – type semiconductor.    
7. What is Fermi’s golden rule?
8. Discuss in detail the dependence of Fermi level on carrier concentration and temperature.
9. What do you mean by occupation probability?
10. Write the expression for the Fermi level energy in n – type semiconductor.

Numerical Problems

Important Notice : 

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