## Physics midterm preparatory exam, ( + 2 ) 2nd year

SUB: PHYSICS, P.U.C.-II, midterm preparatory, date 16.8.2013

TIME: 3.15 Hrs                                                MAXIMUM MARKS: 90

GENERAL INSTRUCTIONS:

All parts are compulsory

Draw relevant diagram/ figure wherever necessary

Numerical problems should be solved with the relevant formula.

### PART A

Question 1 – 10

Answer all the following, 1 mark each ( total 10 )

#### Question 1

Which of the following is a vector?

A. An electric dipole’s electric potential          B. An electric dipole’s charge

C. Electric current                                                D. Electric current density

#### Question 2

Which medium will have a stronger electrostatic force between 2 charges?

A. Medium with $\epsilon =12$                                    B. Medium with $\epsilon =102$

C. Medium with $\epsilon =81$                                  D. Free space, $\epsilon = \epsilon_0$

#### Question 3

Pick only the correct one “between an electron and a positron”

A. The electron has more specific charge

B. The positron has more specific charge

C. Both have equal specific charge

D. For some particles specific charge can’t be determined, so it can’t be said electron or positron has more specific charge

#### Question 4

Chose the correct one

A. Kirchhoff’s loop rule is applied to a junction of incoming and outgoing current

B. According to Kirchhoff’s loop rule a junction of incoming and outgoing current carries a potential proportional to the amount of current flowing through the junction

C. Kirchhoff’s Junction rule can be applied to a single current carrying path in any electric circuit

D. The potential drop in a loop in any electric circuit is zero and its based on conservation of energy

#### Question 5

Chose the correct one

A. Resultant of capacitance in series is more than individual resistances

B. Current division works on the basis of direct proportionality of resistances

C. Voltage division works on the basis of direct proportionality of resistances

D. Resistors in series will add up

#### Question 6

Ohms’ law corresponds to the following

A. Voltage and current are proportional even if resistance varies

B. Conductivity is a ratio of current density and electric field

C. Resistances must add up in parallel combination

D. Linear relation between voltage and current can be accommodated to an arbitrary range of resistances

#### Question 7

If we define a system-of-unit where permittivity of free space is 1 and electric field intensity E value is 1, which is the correct value for energy density?

A. $\frac{1}{2}$                              B. $\frac{1}{3}$

C. 2                                D. 3

#### Question 8

If we define a system-of-unit where capacitance of a configuration is 1 and potential difference of the same is 1 what is the electrostatic energy of the configuration?

A. $\frac{1}{2}$                            B. $\frac{1}{3}$

C. 2                                D. 3

#### Question 9

If $100$ electrons passing through an unit cross section area A constitute a current of $100 \times 1.6 \times 10^{-19}\,\frac{C}{s}$ flowing across it, what’s the drift velocity of the electrons?

A. 1 unit                B. 2 units                 C. 0.5 units                D. 5 units

#### Question 10

A capacitor of $18 \,\mu F$ is filled with dielectric of dielectric strength $K =5$. ( Or permittivity $\epsilon$ ). What’s the new value of capacitance, if a potential difference $V = 1000 \,volt$ is found on the capacitor?

A. $90 \,\mu F$                                                 B. $\frac{18}{5} \,\mu F$

C. $\frac{5}{18} \,\mu F$                                            D. indeterminate

### PART B

Questions 1 – 12

Answer any 10, 2 marks each ( total 20 )

#### Question 1

Define “temperature coefficient of resistance” $\alpha$ of a metal.

#### Question 2

Describe de-Broglie wavelength in 1 or 2 lines and write the formula.

#### Question 3

Define electric current and electric current density.

#### Question 4

Given Bohr radius of hydrogen atom; $a_0$, what would be the radius of the $4^{th}$ excited orbit $(n = 5)$.

#### Question 5

Whats the speed of an electron in a hydrogen atom in terms of speed of light c, if its revolving in the $5^{th}$ orbit; $v_n = v_5$, according to the Bohr’s model of an atom?

#### Question 6

Give example of 2 conservative forces.

#### Question 7

Define atomic number, atomic mass and neutron number. What’s mass of an $\alpha-{particle}$ in terms of $amu$.

#### Question 8

Write out the expression of $n^{th}$ level atomic spectra (energy level) of a hydrogen atom. What energy will be released if the electron jumps from level: $4 \to 1$?

#### Question 9

Write out the expression of $n^{th}$ level atomic spectra (energy level) of a hydrogen atom. What energy will be released if the electron jumps from level: $5 \to 2$?

#### Question 10

What’s the power of a lens whose object distance is $15 \,cm$ and whose image distance is $55 \,cm$.

#### Question 11

What’s the focal length of a convex lens if object distance is $20 \,cm$ and image distance is $30 \,cm$.

#### Question 12

What’s the resistance of a wire that obeys Ohm’s law if it carries a current of $2.5 \,ampere$ when a potential difference of $230\,volts$ is applied across its ends?

### PART C

Question 1 – 12

This question is compulsory  ( total 5 )

#### Question 1

Define electric current and electric current density. State if these two quantities are scalar or vector quantities and explain why. State and explain Ohm’s law. Derive the Ohm’s law in vector form from the scalar form.

Answer any 6 from Question 2  –  8  ( total 30 )

#### Question 2

Derive the electric potential $V$ for the dipole vector $P$, $V_{||}$; in a direction of alignment with the dipole vector, also called End-On configuration. Show that the electric field due to a dipole vector is zero along a line perpendicular to it.

#### Question 3

Derive the magnetic field due to a torroid by using Ampere’s circuital law.

#### Question 4

Define electric flux $\Phi_E$. State and explain Gauss law in terms of charge and flux. Apply the Gauss law to the case of an infinitely straight distribution of charge with linear density of charge $\lambda$. Mention 4 properties of the lines of force. What is signified by the fact that lines of forces are densely packed? Why lines of forces must not intersect?

#### Question 5

Derive the expressions for combination of 3 capacitors in series and parallel. What’s the capacitance of a combination of two capacitors each with capacitance $12 \,\mu F$ connected in series? What’s the value if these are connected in parallel? Derive the energy associated with a capacitor.

#### Question 6

Derive the expression for the capacitance of a configuration where two plates are kept distance $d$ apart when a material of thickness $t$ with dielectric constant $K$ is inserted in-between.

#### Question 7

Derive the magnetic field B of a solenoid by using Ampere’s circuital law.

#### Question 8

State the Ampere circuital law and define magnetic flux. State the Maxwell’s cork screw rule. From the Lorentz force expression derive the force acting on a current element of length $l$ by a magnetic field B.

This question is compulsory  ( total 5 )

#### Question 9

Describe the mechanism of a cathode ray tube with a neat and labeled diagram. Write a short history of how electrons were discovered. What is $X-{ray}$ emission? What are $K_a$ and $K_b$ lines?

Answer any 2 from Question 10 – 12 ( total 10 )

#### Question 10

Describe the Bohr model for the atom and point out its drawbacks. Write the $n^{th}$ level energy of a hydrogen atom. Calculate the emission energy of a hydrogen atom if an electron jumps from $n = 8 \to n = 1$ level. Explain the origin of $K_a$ and $K_b$ lines through electronic transitions.

#### Question 11

Describe the Millikan’s experiment for electron charge $e$. Derive in necessary steps how $e$ would be determined by this set up from various known parameters. Explain your steps with the concepts.

#### Question 12

Threshold wavelength of Tungsten is $2400\,{\AA}$. Tungsten is illuminated by a light of wavelength $1600\,{\AA}$. Whats the value of work function, maximum kinetic energy of electrons and stopping potential? Describe the ideas of photoelectric effect.

### PART D

Question 1 – 2

Answer both questions ( total 10 )

#### Question 1

What is photoelectric effect? Explain what is work function, maximum kinetic energy of electrons, stopping potential and threshold frequency in photoelectric effect. Describe the Thomson’s $\frac{e}{m}$ experiment with neat diagrams and obtain electron speed $v = \frac{E}{B}$.

#### Question 2

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. If $u = 10 \,cm$ and $v = 15 \,cm$, whats the power of the lens?