IGNOU BPHCT-133 June 2022 Previous Year Question Paper

Q1.Answer any five parts : 5x3=15

(a) Write down the electric field due to a uniformly charged non-conducting sphere of radius R carrying charge Q at a point inside it in Cartesian coordinates. Obtain its divergence. 1+2

(b) State Stokes’ theorem. Use it to obtain Maxwell’s equation f E.dl =a J] B.dS Cc Ss in its differential form. 1+2

(c) Determine the electric field due to an electric dipole at the midpoint of its axis. Draw a properly labelled diagram. 241

(d) If the electric potential is zero at a given point, must the electric field at that point also be zero ? Justify your answer giving an example. 3

(e) A parallel plate capacitor is made up of two rectangular plates each having area 6-0 x 107? m? and separated by a distance of 1:0 mm. A dielectric of dielectric constant 3-0 fills up the space between the plates. Calculate the capacitance of the capacitor.

Q2.What is the charge stored on each of its plates if a voltage of 10 V is applied across them ? 241

(f) A toroid with 2000 turns is wound on an iron ring having area of cross-section 400 mm? and mean circumference 1:0 m. Calculate the magnitudes of magnetic intensity H and the magnetic field B when the current through the toroid is 0:25 A. The relative permeability of the iron ring is 1500. 1 5 +1 5 BPHCT-133 2

(g) Apply Lenz’s law to determine the direction of the current induced in a loop kept in a magnetic field, when its area is decreased. Assume that the loop is lying in the plane of this page perpendicular to the magnetic field, which is directed into the page. 3

(h) A plane electromagnetic wave is travelling in vacuum in the positive x-direction. Its frequency is 10 MHz and the amplitude of the associated electric field E is 200 Vm}.

Q3.Write the complete expression of the E field given that it is in the positive y-direction.

Q4.Answer any five parts : 5x5=25

(a) Determine the directional derivative of the scalar field » = x’y? + 3xyz at the point (1, 1, 1D in the direction of the vector

(b) Determine the work done by a force field F = xy?t + yx} in moving an object along the curve y = x” in the xy plane between the points (0, 0) to (1, 1). 5

(c) Using Gauss’s law, explain how you can protect yourself from a lightning strike by sitting inside a closed conducting surface such as a closed car. 5

(d) Consider two points A and B located in a uniform electric field directed along the negative x-axis. The coordinates of the points are xa=5m and xg=10m, respectively. Is the potential difference Vz — Va positive or negative ? Justify your answer. If | Vg — Va | = 10° V, what is the magnitude of the electric field ? 342

(e) A toroid has 1000 turns and a current of 100 mA is flowing in it. If the inner and outer diameters of the toroid are 0-08 m and 0-10 m respectively, calculate the maximum and minimum values of the magnitude of the magnetic field in the toroid. 2 5 +25 BPHCT-133 4

(f) A capacitor is made up of two hollow concentric metal spheres of radii R, and Rg such the Ry > R,. The region between the concentric spheres is filled with a dielectric material of dielectric constant K and the outer sphere is earthed. Determine the capacitance of the capacitor. 5

(g) An electric generator consists of a 50 turn square coil of side 1-0 m. The coil turns at 50 rps. Calculate the magnitude of magnetic field required for a peak output voltage of 270 ५. 5

(h) The magnetic field associated with a uniform plane electromagnetic wave is given by B =(2x 10-8 1) sin (100 ny — ot) The wave is travelling in a dielectric medium for which e€=9) and ॥5॥७- Calculate the speed of the wave in the medium, and the refractive index and dielectric constant of the medium. Write the complete expression of the electric field associated with the wave in the dielectric medium.

Q5.Answer any two parts: 2x5=10

(a) Apply Gauss’s law to determine the electric field due to a uniformly charged non-conducting sphere of radius ‘a’ at a point inside it. The charge on the sphere is

Q6.Q. 5

(b) Using Biot-Savart’s law, derive the expression for magnetic field due to an infinite current-carrying wire. 5

(c) Define the energy density of the electromagnetic field. Starting from the integral form of Poynting’s theorem, show that 1+4 Physical Constants : &) = 8°85 x 10-1? C2? N-} mr? ce=3x108 ms? Yo -2x10-7 Tma? BPHCT-133 6 f E.dl =a J] B.ds Cc 8 BPHCT-133 8 o= x2y? + 3xyz (@) aa 8a F =xy?] + yx} gw fig & xy BPHCT-133 10 B =(2x 10-8 1) sin (100 my — wt) V.S =-2 (Uy + Upp) c=3x108 ms? Yo =2% 1077 TmAt