IGNOU BPHCT-133 December 2023 Previous Year Question Paper

Q1.Answer any five parts : 3 each

(a) The potential at any point (x, y, z) is given by: (x? +y74 2) where k is a constant. Find the components of the force along x, y and z-direction and hence obtain an expression of the force induced at (x,y,z) by the potential

(b) Calculate the work done by the force : F=ayi-y?j in moving an object along the curve y= x? in the xy-plane from (0, 0) to (1, 1).

(c) The hydrogen atom consists of an electron and a proton separated by an average distance of 5.3x10'm. Calculate the magnitude of the electrostatic force between the electron and proton taking them to be at rest. (१) A particle carrying a charge of 3x10°C is enclosed in a cubical Gaussian surface of side 0.25 m. Calculate the electric flux through the surface of the cube.

(e) The radius of a gold nucleus is 6.6 x 10-15 m, and the atomic number Z of gold is 79. Assuming that the nucleus acts as a point charge and electronic charge e=1.6x 107१0, calculate the electric potential at the surface of a gold nucleus.

(f) A dielectric block is polarized such that : P =2.5x107 [sat +j+k|Cm® Calculate the bound volume charge density for the block.

(g) An electric generator consists of 20 turns square wire coil of side 50 cm. The coil is turned at 50 revolutions per second to produce the standard 50 Hz a. c. produced in India. What must the magnitude of the magnetic field be for the peak output voltage of the generator to be 300 V?

(h) What rate of change of current in solenoid having self-inductance 10 mH produces a self-induced e.m.f. of 50 mV in it ?

Q2.Answer any five parts : 5x5=25

(a) Show that the electromagnetic field described by : E = E) Zcoskx.cosky.cos at and B=Bo [$ coskx.sinky— sin kx.cos ky] sin wt will satisfy the Maxwell’s equation : 98 =VxE if Ey = 2 cBo and w = /2 ck.

(b) A uniformly charged disc having charge Q and radius R is rotating with constant angular velocity of magnitude o. Show that its magnetic dispole movement has magnitude + (9०४2).

(c) Acurrent of 0.70 A is flowing in a circular coil of radius 0.02 m. Calculate the magnitude of the magnetic field due to this coil at a point 1.0 m away from the centre of the coil along its axis.

(d) A dielectric of dielectric constant 2.0 is filled in the gap between the plates of a capacitor. Calculate the factor by which the capacitances is increased if the dielectric is only sufficient to fill up 2/5 of the gap.

(e) Three particles each having charge + Q are placed at the vertices of an equilateral triangle with each side of length R. Calculate the magnitude of the net electric field at the mid point of any side of the triangle.

(f) A flat sheet of charge of surface area A has uniform surface charge density o. An electrostatic force of magnitude

Q3.0x10°2N pointing in a perperdicular direction away from the sheet, is exerted on an electron of a perpendicular distance of 0.02 m from its centre. Calculate the net charge on the sheet for A = 2.0 m2.-

(g) Evaluate : > 3S ff, V Ads where V = 2xcos? yi +5xz j+2zsin? yk and S is the surface of a sphere with its centre at the origin and radius 2 units.

(h) A two-dimensional force field is defined as : x+y where k is a constant. Calculate the work done by this force in taking a particle from point A (1, 0) to B (0, 1) along a straight line.

Q4.Answer any two parts : 2x5=10

(a) Consider an electric dipole AB of length '2a' and a point P at a distance of 'r' from the mid point C of the dipole and the line CP is making an angle of @ with respect to the dipole axis. Find the electric potential at P.

(b) Consider a parallel plate capacitor with dielectric material inserted between its plates. Deduce an expression for the capacitance of such a system when the space between the plate is only partially filled by the dielectric.

(c) What do you understand by the term ‘displacement current’ ? Consider a parallel plate capacitor that is being charged by a constant current ‘i. Show that the displacement current is same as the current ‘i’ charging the capacitor. Physical constants : —1 =8.99x10°Nm?C 47760 €9= 8.85x10 ” 02 ]ए का? bp =1.26x10 NA? e=1.6x10°%C c=3x108 ms + P=2.5x10"[3ei + j+k]Cm?