IGNOU BPHCT-133 December 2022 Previous Year Question Paper

Q1.Answer any five parts : 5x3=15

(a) The potential that represents a force is where k is a constant. Using the definition F =- VV, calculate the components of this force. 3

(b) Obtain a function हे

(0) which satisfies the relation : a A 4200 =ti + sin (xt) j +

(2) k dt t Given that a

(1)=31 + j +4k. 3

(c) What is the electric field of a particle having charge — 4-0 x 10-9 C at a point 2:0 m away from it ? Determine the electrostatic force exerted on an electron placed at that point. 3

(d) The electric flux through a closed spherical Gaussian surface of radius 01m surrounding a charged particle is equal to 1500 Nm2 C-1, Determine the value of the charge on the particle. 3

(e) What is the difference between polar and non-polar molecules ? Give one example each. 3

(f) Distinguish between diamagnetic, paramagnetic and ferromagnetic materials. 3

(g) A solenoid of length 1:0 m and diameter 0-2 m has 100 turns of wire. What is the self-inductance of the solenoid ? 3

(h) Explain briefly, the asymmetry in Gauss’s laws for electric and magnetic fields.

Q2.Answer any five parts : 5x5=25

(a) Using Stokes’ theorem, evaluate | x al. where a = 224 + yak and C is the boundary of a triangle OPQ with vertices O(0, 0, 0), P(O, 2, 0) and Q(O, 2, 1). 5

(b) Apply the Divergence theorem to compute {J A : as where S is the surface of the cylinder x? + y? = a? bounded by the planes > A A A z=0,z=band A =xi -yj +zk. 5

(c) Two point charges +4q and +9q are placed at rest a distance R from each other. Determine the position of a charge +q placed on a straight line joining these two charges, if it is in equilibrium. 5

(d) A uniform electric field of 4-0 x 103 NC-1 is in positive x-direction. A positive point charge of 1-0 uC is released from rest at the origin. Calculate the potential difference V

(4) - V

(0). What is the change in the electrostatic potential energy of the charge when it is moved from x = 0 tox=4m? 3+2

(e) Consider a parallel plate capacitor made up of two rectangular plates of area of cross-section 6-45 x 10-4 m? and separated by a distance of 3-0 x 10-3 m. A voltage of 10 V is applied across the plates. If a dielectric material of dielectric constant 5-0 is introduced between the plates of the capacitor, calculate the charge stored on each plate. 5

(f) A square current loop of side 3 cm consists of 50 turns and carries a current of 1A. When kept in a uniform magnetic field it experiences a torque of 3x10-3 Nm resulting in making an angle of 30° of its plane with respect to the magnetic field. Calculate the magnetic field. 5

(g) Obtain the maximum value of displacement current in a parallel plate capacitor made of plates of area 1:0 m?. It is given that the electric field between the plates is E = Eg cos wt with Eg = 5-0 V and frequency 10 MHz. 5 BPHCT-133 4

(h) The electric field given by B = (600 Vm-)$ [eos (100 y - at)] represents the electric field of a plane electromagnetic wave in a charge-free and current-free region. Determine the wavelength and frequency of the wave, and the direction of its propagation. Calculate the associated magnetic field.

Q3.Answer any one part : 1x10=10

(a)

(i) State Gauss’ law. An infinitely long uniformly charged solid cylinder of radius R has positive volume charge density p. Determine the electric field at a point inside the cylinder. 5 Gi) Using Biot-Savart law, derive an expression for the magnetic field at a point P located a distance of R from a wire AB carrying a current I. What would be the magnetic field if the wire is of infinite length ? 5

(b) Obtain the conditions for the following time-varying electric and magnetic fields to satisfy the Maxwell’s equation in vacuum with no source charges or currents : 10 > aA E = jE sin (z-vt), B = iBgsin (z—-vt). Physical Constants : 1 =9x 109 Nm? Cc? 47250 -e=-16x10!%C &y = 8:85 x 10°12 C2 N} m? ॥0 = 1:26 x 10° Hm"? BPHCT-133 6 Oe (x? + y74 2?) पड =ti +sin (xt) j +

(2) k Paysai+j 44k. 3

(7) aa - 40 x 10° C a UG aT a उससे BPHCT-133 8 OG, 0, 0), P(O, 2, 0) HR QO, 2, 1) z | 5 aig 10 MHz@ | 5 BPHCT-133 10 E = jEpsin (z—-vt), B = iBpgsin (z—vt). — 9% 109 Nm? Cc? 47250 -e=-16x1019C &) = 8:85 x 1071? C? N} m? ॥0 = 1:26 x 10° Hm"?