Slight typo/omission is present in 1 or 2 questions. It will be rectified. Subsequent question papers will have the correct version.

SUB: PHYSICS MARKS: 50

CLASS: II PUC TIME: 1.5 Hrs

**PART-A**

**Total 25 marks **

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(**Compulsory, very short-answer questions**)

## Each carries 1 mark. Answer all. (1×5)

1. If two charges are placed a distance r apart in a **dielectric medium** and in **free-space** where will be the **Coulomb’s interaction** be stronger?

2. What’s the **Electric Potential of a Dipole Vector** in the **vertical direction** to it?

3. What is the **work done** when a charge makes a trajectory **on an equi-potential surface**?

4. Write the **de-Broglie formula for wavelength** of a wave-particle if its momentum is p?

5. What’s the relation between **angle of incidence** and **angle of reflection**?

(**Optional 10 out of 18, short-answer questions**)

## Answer any TEN questions, 2 marks each. (2×10=20)

**Electrostatics**

6. State how density of **electric lines of force** is related to the **Electric Field Vector intensity E. **Also mention another three properties of the lines of forces.

7. Write the vector expression for Coulomb’s law and state 3 forces that are conservative forces by nature.

8. What happens to the charge on a conducting shell? What happens to lines of forces when a conducting shell is present in the path of the lines of forces?

9. How one defines the direction of a Dipole Vector? Define a unit dipole vector p. Write the expression for dipole vector by using p and the **magnitude of charge = 3 Q** and separation between the charge as 1 AU, where **AU is the unit of distance** and 1 AU is the distance of the Sun from the earth. {This is a brain teaser}

10. Write the expression for the Electrostatics Potential of a point charge. Calculate the potential for a Nitrogen nucleus at a distance of 1 femto-meter (1 fm = 10^{-15 }meters) {Z _{nitrogen}=14}. Express this in terms of energy, in unit of Joule, by multiplying to the potential the charge of an alpha-particle = 2e.

11. Define **flux of the uniform electric field vector****F**. Write out Gauss law of electrostatics.

12. A charge is placed on a line which intersects the axis of a **Dipole Moment Vector** P by 90^{0} angle. What will be the potential V and electric field E at this point if this point is distance r apart from the center of the dipole moment?

13. A charge is placed on a line which is parallel to the axis of a **Dipole Moment Vector** P. What will be the potential V and electric field E at this charge’s location if this point is distance r apart from the center of the dipole moment?

14. What’s the energy of an alpha particle if we place it in a potential difference of 100 Volt assuming its at rest at this location? What will be the energy of a proton if its placed at the same location at rest.

15. Write the expression for the **electric potential of a dipole** P when the point of reference where we determine the potential is **on the plane of the dipole** so that its **distance r apart** from the **center of the dipole**. Differentiate this equation to obtain the **electric field vector** at this point. Take the angle of the reference line wrt Dipole-Axis asJ.

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**Atoms**

16. Define atomic number, atomic mass and neutron number. What’s the atomic number and atomic mass of Oxygen?

17. Write out the complete expression of **n-th level** atomic spectra {**energy level**} of a Hydrogen atom. What energy will be released if the electron jumps from **level=3 to level = 2**. ?

18. In what **energy** band will a spectrum from a star appears if a star is known to radiate collapse of Hydrogen atom of **level 2 to ground state**? What will be the frequency of such radiation?

19. How many atoms are there in our periodic table as of this year? Name two radioactive elements. Mention in a sentence how radioactivity of Carbon is useful.

**Ray Optics and Instruments**

20. Write out the mirror equation. If an image is at 10 cm and object at 100 cm what’s the focal length of the mirror?

21. If **angle of incidence is 30 ^{0} **and

**angle of refraction is 15**what will be the refractive index of the medium?

^{0}22. Write in 2-3 sentences what’s **Total Internal Reflection (TIR)**. Which of these is not an example of TIR? Mirage, Prism, Diamond, Optical Fiber, Lightening, Magnetic induction.

23. What’s the mathematical expression for the power of a lens? If the focal length of a lens is 150 mm, what’s the power of this lens?

**PART-II**

**Total 25 marks **(**Optional, 5 out of 8, Long-answer questions**)

SECTION-A {Electrostatics}

## Each carry 5 marks, answer only three (5×3)

**Question 1**

Derive a) the **Electric Field Vector ****E _{||}**

**for the**

**Dipole Vector**

**P**in a

**direction of alignment with the Dipole Vector**, also called

**End-On configuration**b) the scalar potential V

_{^}due to the dipole in a

**vertical direction from the center of the dipole**.

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**Question 2**

Derive a) the **Electric Field vector Potential **E_{^}for the **Dipole Vector** **P** in a vertical direction from the center of the dipole, also called **End-On configuration** b) the scalar potential V(r) in a general direction **at angle ****J to the Dipole**.

**Question 3**

Define **Electric flux ****F (Phi)** in 1 or 2 lines and write out expression for it for a uniform** electric field E**. State **Gauss Law** in terms of charge and flux. State the mathematical vector form of **Coulomb’s law of electrostatics force**. What’s the flux of a vector if it is normal to the area vector?

**Question 4 **

Define **Lines of force** and **flux of a vector**. State **Gauss law** and derive its mathematical form by considering **spherical symmetry**.

SECTION-B {Atoms}

## Each carry 5 marks, answer only one. (5×1)

**Question 5**

Obtain an expression for the Nuclear Size of an atom by solving for **distance of closest approach (****r)** which is also known as **Impact Parameter** (say**l**). Use an incoming alpha-particle of mass m_{α} and charge **q** that’s deflected by the presence of a nucleus of atomic number Z to obtain **l. **Now replace the variables by some numerical: m_{α = }_{6.8×10}^{-27}kg, e = 1.6 x 10^{-19 }coul, Z=10, and v_{α}= 2.50×10^{7} m/s. Express the answer in Femto-meters.

**Question 6 **

A proton has a radius R and the charge Q is uniformly distributed. Use **Bohr’s atomic energy level formula **for the 1^{st} excited state {**n=2**} energy of the Hydrogen-atom.

SECTION-C {Ray Optics and Optical Instruments}

## Each carry 5 marks, answer only one. (5×1)

**Question 7**

State the **mirror equation** and **thin lens formula**. For each case determine the **focal length** if the **object** distance is 100 cm and **image** distance is 25 cm.

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**Question 8 **

Draw a simple and neat diagram showing a **convex lens, optical center and focal point** {Focus}. Now define **power of a lens** and obtain an expression for it.