PREPARATORY CLASS EXAMINATION FOR MIDTERM – 2013 (16 Aug 2013)

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

## Each sub-question carries 1 mark.  Answer all.

### (a)

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

### (b)

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, $\epsilon = \epsilon_0$

### (c)

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

### (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 in 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)

Ohm’s 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

### (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 configuration?

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

C. 2                                D. 3

### (i)

If $100$ electrons passing through an unit cross section area A constitute a current of $100\times 1.6 \times 10^{-19}\hspace{2pt}\frac{C}{s}$ flowing across it, what’s the drift velocity of the electrons?

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

### (j)

A capacitor of $18\hspace{2pt}\hspace{2pt}\mu F$ is filled with dielectric of dielectric strength $K=5$. (Or permittivity $\epsilon$). What’s the new value of capacitance, if a potential difference $V=1000\hspace{2pt}volt$ is found on the capacitor?

A. $90\hspace{2pt}\hspace{2pt}\mu F$                                                 B. $\frac{18}{5}\hspace{2pt}\hspace{2pt}\mu F$

C. $\frac{5}{18}\hspace{2pt}\hspace{2pt}\mu F$                                               D. indeterminate

## Each sub-question carries 1 mark.  Answer all.

### (k)

Define ‘temperature coefficient of resistance $\alpha$‘ of a metal.

### (l)

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

### (m)

Define electric current and electric current density.

### (n)

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

### (o)

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?

### (p)

Give example of 2 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 is independent of the path taken”.

### (q)

Define atomic number, atomic mass and neutron number. What’s mass of proton in terms of $amu$.

### (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 level: $3 \to 2$?

### (s)

The radioactive elements always obey a relation of decay which determines their half-life period $\big(T_{\frac{1}{2}}\big)$ 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 $0.62 \hspace{2pt}hour$ and the half-life of $^{38}Sulphur$ is $2.48\hspace{2pt}hour$ while $^{38}Argon$ is a stable nuclei. We have a $10000$ atoms from each at $5:15\hspace{2pt}PM$. We look at them again after two hours. We still have $10000$ Argon atoms. Between Sulphur and Chlorine which is now available in less number?

# PART II

## This question is compulsory  ( total 7 )

### Question 2

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. Write the expression for drift velocity.

## Answer any two  ( total 6 + 6 = 12 )

### Question 3

Derive the electric field vector $\vec{E}$ for the dipole vector $\vec{P}$ i.e., $E_{||}$ and $E_{\perp}$; in a direction of alignment with the dipole vector, also called End-On configuration and in a direction vertical to it, called as Broad-on configuration.

### Question 4

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 $\lambda$. Describe the properties of the lines of forces. Why lines of forces must not intersect?

### Question 5

Derive the expressions for combination of 4 capacitors in series and parallel. Whats the capacitance of a combination of two capacitors each with capacitance $10 \hspace{2pt}\mu F$ connected in series. Whats the value if these are connected in parallel. Derive the energy associated with a capacitor.

## Answer any 2  ( total 6 + 6 = 12 )

### Question 6

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 $\alpha_m = 4\hspace{2pt} {amu}$ and charge $q=2 \times 1.6 \times 10^{-19}\hspace{2pt}C$ that’s deflected by the presence of a nucleus of atomic number $Z=14$ to obtain $b$. Describe the Geiger Marsden experiment. What are drawbacks of the Rutherford’s model?

### Question 7

Describe nuclear fission. What’s the cause of Sun’s energy, fusion or fission? What about the stars Alpha-centauri A, B, C? Write the charge (in units of electronic charge $e$) and mass (in atomic mass unit $u$, or $\frac{eV}{c^2}$, eg $\frac{MeV}{c^2}$) of each of these elementary particles. photon, $\alpha-{particle}$, gamma-rays ( $\gamma$), neutrino ( $\nu$), proton, electron, in a table. Which of these particles will experience the strongest electrostatic force?  Which of them will experience the lowest force? Arrange them in that order.

### Question 8

Explain what’s radioactivity. Derive the radioactive decay law and define half-life with explanations of steps. Give example of four radioactive elements. Explain why radioactivity is harmful towards living organisms.

## 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?

## Answer any 2  ( total 7 + 7 = 14)

### 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 $n = 10 \to n = 3$ level. What are $K-a$ and $K_b$ lines in characteristic X-ray emission? Explain their origin 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

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 the electron speed $v=\frac{E}{B}$.