41. A cylindrical rod of length L and radius r, made of an inhomogeneous dielectric, is placed with its axis along the Z-direction with one end at the origin as shown below.
If the rod carries a polarization $$\overrightarrow {\bf{P}} = \left( {5{z^2} + 7} \right){\bf{\hat k}},$$ the volume bound charge inside the dielectric is
If the rod carries a polarization $$\overrightarrow {\bf{P}} = \left( {5{z^2} + 7} \right){\bf{\hat k}},$$ the volume bound charge inside the dielectric is
42. The figure shows a constant current source charging a capacitor that is initially uncharged.
If the switch is closed at t = 0, which of the following plots depicts correctly the output voltage of the circuit as a function of time?
If the switch is closed at t = 0, which of the following plots depicts correctly the output voltage of the circuit as a function of time?
43. A coaxial cable of uniform cross-section contains an insulating material of dielectric constant. The radius of the central wire is 0.01 m and that of the sheath is 0.02 m. The capacitance per kilometre of a cable is
44. A parallel plate capacitor is being discharged. What is the direction of the energy flow in terms of the Poynting vector in the space between the plates?
45. Two point charges Q1 = 1 nC and Q2 = 2 nC are kept in free space such that the distance between them is 0.1 m. Which of the statements is correct?
46. The magnetic field (in A/m) inside a long solid cylindrical conductor of radius a = 0.1 m is $$\overrightarrow {\bf{H}} = \frac{{{{10}^4}}}{r}\left[ {\frac{1}{{{\alpha ^2}}}\sin \left( {\alpha r} \right) - \frac{r}{\alpha }\cos \left( {\alpha r} \right)} \right]\hat \phi ,$$ where, $$\alpha = \frac{\pi }{{2a}}.$$ What is the total current (in ampere) in the conductor?
47. Four point charges are placed at the corners of a square whose centre is at the origin of a Cartesian coordinate system. A point dipole $$\overrightarrow {\bf{p}} $$ is placed at the centre of the square as shown in the figure. Then,
48. A plane electromagnetic wave travelling in vacuum is incident normally on a non-magnetic, non-absorbing medium of refractive index n. The incident (Ei), reflected (Er) and transmitted (Et) electric fields are given as
Ei = E exp[i(kz - ωt)], Er = E0r exp[i(krz - ωt)], Et = E0t exp[i(ktz - ωt)]
If E = 2 V/m and n = 1.5, then the application of appropriate boundary conditions leads to
Ei = E exp[i(kz - ωt)], Er = E0r exp[i(krz - ωt)], Et = E0t exp[i(ktz - ωt)]
If E = 2 V/m and n = 1.5, then the application of appropriate boundary conditions leads to
49. An electric field applied along the length of a long, cylinder produces a polarization P. The depolarization field produced in this configuration is
50. Consider a set of two stationary point charges q1 and q2 as shown in the figure. Which of the following statements is correct?
