**MIDTERM EXAMINATION – 2013 – 14 (August)**

**PHYSICS (Theory)**

**Paper – 1**

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

**General Instruction:**

**(i)** Answer all question in Part I and six questions from Part II, choosing two questions from each of the Section A, B and C.

**(ii)** All working including rough work should be done on the same sheet as, and adjacent to the rest of the answer. DO NOT WRITE ON QUESTION PAPERS.

**(iii)** The intended marks for questions or parts of questions are given in brackets []. (Material to be supplied: Log tables including Trigonometric functions)

**(iv)** A list of useful physical constants is given at the end of this paper.

** **

**PART I (Compulsory)**

**Q 1:**

**Answer all questions briefly and to the point:**

**(i).** Explain the statement ‘**Relative permittivity of water is 81’**.

**(ii).** Draw (at least three) electric lines of force due to an **electric dipole**.

**(iii).** Find the value of resistance X in the circuit below so that the junction M and N are at the same potential. (See Figure 1 below)

**(iv).** State the superposition principle of any vector, eg the electric field E.

**(v).** 3 charges are located in a region and interacting with each other via Coulomb’s attraction/repulsion. If 1 charge does not influence the amount by which the 2^{nd} and 3rd charge interact by what name this properties is known as?

**(vi).** Write an equation of Lorentz force F acting on a charged particle having charge q+q’ moving in a magnetic field 2B with a velocity 3v in vector form.

**(vii).** How many alpha-particles can produce a charge of 1602 x 10 ^{-19} Coul?

**(viii).** An a.c. generator generates an emf ‘e’ given by : e = 311 Sin (100.π.t) volt. Whats the frequency of this oscillation? Whats the amplitude of oscillation? State in SI Units.

** (ix).** State if this is correct or incorrect. In a pair production process charge is not conserved but in a pair annihilation process charge and energy are both conserved.

**(x).** In a typical lightning bolt 2.5 x 10^{4} A exists for 20 µs, what’s the amount of charge transfer?

**(xi).** What’s the distance between point charge 26 µC and -47 µC if the electrostatic force of attraction between them is 5.7 N.

**(xii).** A current of 0.300 A through your chest can send your heart into fibrillation, ruining normal rhythm of heartbeat and disrupting flow of blood (thus oxygen) to your brain. Such a current persists for 2 minutes. How many conduction electrons passed through your chest?

**(xiii).** In a beta decay (a) proton transforms to neutron, what will be produced? Electron or positron? (b) Neutron transforms to proton, now what will be produced? Electron or positron?

**(xiv).** How many mega-coulombs of positive charges are available in a mol of neutral molecular Hydrogen Gas (H_{2}).

**(xv).** Find the momentum of a photon of energy 3.0 eV.

**(xvi). **The half life of a certain radioactive element is 8 hours. If Mr Soham starts with 32 g of this element, how much of the sample will be left behind at the end of one day?

**(xvii).** If a hydrogen atom goes from 3rd excited state to 11th excited state, what kind of radiation (visible light, ultra violet, infrared, etc.) is emitted?

**(xviii).** Where in our universe is the thermo-nuclear energy being released naturally?

**(xix).** What’s the torque on a dipole if the electric field of 100 Volts/meter is at an angle of 30 degree to the dipole of strength 2 Coul-meter.

**(xx).** What’s the potential energy of a dipole present in an electric field of 100 Volts/meter which is at an angle of 30 degree to the dipole of strength 2 Coul-meter.

**PART II**

**Answer six questions in this part, choosing two questions from each of the Sections A, B and C**

**SECTION A**

**(Answer any two questions) 8×2**

**Q 2:**

**(a)** With the help of a labelled diagram, obtain an expression for the electric field intensity ‘E’ at a point P in broad side position (i.e. equatorial plane) of an electric dipole.

**(b)** Find the electric charge Q1 on plate of capacitor C1, shown in Figure below:

**(c) **

**(i)** What is meant by:

**(1)** Drift velocity and

**(2)** Relaxation time?

**(ii)** A metallic plug AB is carrying a current I (see Figure4 below). State how the drift velocity of free electrons varies, if at all, from end A to end B.

** **

**Q 3: (a)** Figure 5 below shows a uniform manganin wire XY of length 100 cm and resistance 9 ohm, connected to an accumulator D of emf 4 V and internal resistance 1 ohm through a variable resistance R, E is a cell of emf 1.8 V connected to the wire XY via a jockey J and a central zero galvanometer G. It is found that the galvanometer shows no deflection when XJ = 80 cm. Find the value of R.

**(b)** Obtain an expression for magnetic flux density ‘B’ at the center of a circular coil of radius R and having N turns, when a current I is flowing through it.

**(c) **The electric potential difference between ground and a cloud is 1.2 x 10^{9} V, in units of electron-volts what’s the magnitude of change in electric potential energy of an electron that moves between ground and cloud.

** **

**Q 4:**

**(a)** The electric field in a region of space has the components E_{y} = E_{z}=0 and E_{x} = (4.000 N/C) x. Point A is on y axis y = 3.00 m and point B is on the x axis at x = 4.00 m. What’s the potential difference **V _{B} – V_{A}**

**(b) **A wire of Nichrome (Nickel, chromium and iron alloy used commonly for heating) is 1.0 m long and 1.0 mm^{2} in cross-section area. It carries a current of 4.0 A when a 2.0 V potential difference is applied between its ends. Calculate the conductivity s of Nichrome.

**(c) **A student kept his 9.0 V, 7.0 W radio turned on at full volume, from 9 PM to 2 AM. How much charge went through it?

** **

**SECTION B**

**(Answer any two questions) 8×2**

**Q 5:**

**(a) **A certain X-ray tube operates at a current of 7.00 mA and a potential difference of 80.0 kV What is its power in watts? ** **

**(b)** Four 18.0 ohm resistors are connected in parallel across a 25 V battery, what is the current through the battery.

**Q 6: **If you are to connect resistors **R _{1}, R_{2} **and

**R**with

_{3}**R**to a battery arrange according to amount of current passing through them, larger current first and smaller current after that, if they can be connected

_{1}> R_{2}**individually**, in

**series**or in

**parallel**.

**Q 7:**

**(a**) How fast an electron must move to have a kinetic energy equal to energy of a photon in Sodium light at wavelength 590 nm?

**(b)** Lets say we have X-rays of wavelength 35.0 pm. What’s the (i) frequency (ii) photon energy and (iii) photon momentum (magnitude) associated with this X-ray?

**(c) **What’s maximum kinetic energy of electrons ejected from a certain material with its work function 2.3 eV when radiation of frequency 3.0 x 10^{15} Hz is incident upon it?

**SECTION C**

**(Answer any two questions) 9×2**

**Q 8:**

**(a)** Electrons, initially at rest, are passed through a potential difference of 2 kV. Calculate their:

**(i)** Final velocity and

**(ii)** de Broglie wavelength

**(b)** What are characteristic X rays? How are they different from continuous X rays? Give any one difference.

**(c)** Wavelength of the 1st line (Ha) of Balmer series of hydrogen is 656.3 nm. Find the wavelength of its 2nd line (Hb).

**Q 9:**

**(a)** Plot a labelled graph of |Vs| where Vs is stopping potential of photoelectrons versus frequency ‘f’ of incident radiation. How will you use this graph to determine the value of Planck’s constant? Explain.

**(b) **

**(i)** Define ‘unified atomic mass unit’.

**(ii)** Find the minimum energy which a gamma ray photon should possess so that it is capable of producing an electron positron pair.

**(c)** Fission of U – 235 nucleus releases 200 MeV of energy. Calculate the fission rate (i.e. no. of fissions per second) in order to produce a power of 320 MW.

**Q 10: **

(a) What’s the ratio of the shortest wavelength of Balmer series to the shortest wavelength of the Lyman series?

(b) What are the (i) energy (ii) magnitude of momentum, and (iii) wavelength of the photon associated with spectral emission of H-atom transition; n=3 state to n=1 state?