MIDTERM EXAMINATION – 2013 – 14 (August)

PHYSICS

PAPER I

(THEORY)

(Three hours)

Candidates are allowed additional 15 minutes for only reading the paper. They must NOT start writing during this time.

Answer all questions in Part I and eight questions in Part II, choosing two questions from each of the three sections A, B and C.

All working including rough work should be done on the same sheet as, and adjacent to, the rest of the answer.

The intended marks for questions or parts of questions are given in brackets [ ].

## PART-I

Total 10 + 10 = 20 marks

Each sub part of a question carries 1 mark.  Answer all. (10)

#### Question 1 [ Objective, 10 × 1 ]

(a)

Which of the following drops faster?

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

C. A point charge’s electric field                            D. A point charge’s electric potential

(b)

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

A. Medium with $\epsilon = 10$                       B. Medium with $\epsilon = 100$

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

(c)

Pick only the correct one “between an $\alpha-{particle}$ and a proton”

A. The $\alpha-{particle}$ has more specific charge.

B. The proton has more specific charge.

C. The $\alpha-{particle}$ has more specific charge if its immersed in a medium with permittivity $\epsilon_0 = 81$ than in free space.

D. The proton has more specific charge if its immersed in a medium with permittivity $\epsilon_0 = 81$ than in free space.

(d)

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.

(e)

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

(f)

Ohms’ law corresponds to the following

A. Voltage and current are proportional even if resistance varies.

B. Conductivity is the 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.

(g)

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

(h)

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 capacitor?

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

C. 2                                D. 3

(i)

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

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

(j)

A capacitor of $16 \,\mu F$ is filled with dielectric of dielectric strength $K = 5$ — or permittivity $\epsilon$. Whats the new value of capacitance given a potential difference $V = 1000 \,volt$ is found on the capacitor.

A. $80 \,\mu F$                                                B. $\frac{16}{5} \,\mu F$

C. $\frac{5}{16} \,\mu F$                                              D. indeterminate

#### Question 2 [Short answer, 10 X 1]

(k)

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

(l)

Describe de-Broglie wavelength in 1 or 2 lines and write the formula that we use for this idea.

(m)

Define Bohr radius of hydrogen atom; $a_0$, and state its value in pico-meter.

(n)

Given Bohr radius of hydrogen atom; $a_0$, what would be the radius of the $5^{th}$ excited orbit $(n = 6)$.

(o)

Whats the speed of an electron in a hydrogen atom in terms of speed of light c, if its revolving in the $7^{th}$ orbit; $v_n = v_7$, according to the Bohr’s model of an atom?

(p)

Give example of 3 conservative forces. A conservative force is defined through the following; “The work done in a conservative force field during a circular voyage is zero, as such work done are independent of the path taken”.

(q)

Define atomic number, atomic mass and neutron number.

(r)

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 $5^{th} \to 2^{nd}$ level?

(s)

Cigarette smoking causes cancer as cigarette contains radioactive elements during their preparation. The radioactive elements always obey a relation of decay which determines their half-life period if an initial sample is given with a specified number of radioactive elements. Write out the simple expression ( formula ) for radioactive decay in terms of half-life?

(t)

The half-life of $^{38}Chlorine$ is $0.62\,hrs$ and the half-life of $^{38}Sulfur$ is $2.48\,hrs$ while $^{38}Argon$ is a stable nuclei. We have $1000\,atoms$ from each at $5:15\,P.M.$. We look at them again after two hours. We still have $1000\,Argon\, atoms$. Between Sulfur and Chlorine which is now available in less number?

## PART — II

Total 50 marks ( Opt; 6 of 9. Compulsory 2 )

### SECTION — A

This question is Compulsory   ( 7 × 1 )

#### Question 3

Define electric current and electric current density. State and explain Ohm’s law. Derive an expression for drift velocity.

Answer any two   ( 6 × 2 )

#### Question 4

Derive the electric field vector $\vec{E}$ for the dipole vector $\vec{P}$, vector $\vec{E}_{||}$; in a direction of alignment with the dipole vector, also called End-On configuration. Derive the electric field scalar potential V for the dipole vector $\vec{P}$, $V_{\perp}$; in a direction perpendicular to the dipole, also called Broad-On configuration.

#### Question 5

Define electric flux $\Phi_E$ and write out expression for it for a uniform and non-uniform electric field 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 $\lambda$. State the mathematical vector form of Coulomb’s law of electrostatics force.

#### Question 6

Derive the expressions for combination of 3 capacitors in series and parallel. Whats the capacitance of a combination of two capacitors each with capacitance $5\,\mu F$ connected in series. Whats the value if these are connected in parallel. Derive the energy associated with a capacitor.

### SECTION-B

Answer any two   ( 6 × 2 )

#### Question 7

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 $b$ ). Use an incoming $\alpha-{particle}$ of mass $m_{\alpha}$ and charge $q$ that’s deflected by the presence of a nucleus of atomic number $Z$ to obtain $b$. Use the idea of Rutherford’s model to explain why there is a nucleus and why most of the space inside atom is empty.

#### Question 8

Describe nuclear fusion. What’s the cause of sun’s energy, fusion or fission? What about the stars Alpha-centauri? Write the charge ( in units of electronic charge $e = 1.6 \times 10 ^{-19}\,C$ ) and mass ( in atomic mass unit $u$, or $\frac{eV}{c^2}$, eg $MeV$ ) of each of these elementary particles. Photon, $\alpha-{particle}$ $\gamma-{rays}$ ( gamma-rays ), $\nu$ ( neutrino ), proton, $e^{-}$ ( electron ), in a table.

#### Question 9

Derive the Radioactive decay law and define half-life $T_{\frac{1}{2}}$. Give example of two radioactive elements. Explain why radioactivity is harmful towards living organisms.

### SECTION-C

This question is Compulsory   ( 5 × 1 )

#### Question 10

Describe the mechanism of an X-ray tube. Is X-ray deflected by electric or magnetic field? Explain why.

Each carry 7 marks, answer only two   ( 7 × 2 )

#### Question 11

Describe the Bohr model for 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 $n = 6 \to n = 5$level.

#### Question 12

Describe the Thomson’s $\frac{e}{m}$ experiment by mutually perpendicular set-up of electric field and magnetic field; E and B. Derive in necessary steps how $\frac{e}{m}$ would be determined by this set up from various known parameters such as E and B values.

#### Question 13

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. Who discovered photoelectric effect? Which scientist successfully explained this effect?