Using Maxwell's equations in free space, derive the wave equation for the x-component of the electric field vector.
See Answer →Discuss the B-H curve for a ferromagnet.
See Answer →Using Biot-Savart's law, obtain an expression for the magnetic field due to electric current flowing in a long straight wire at a distance R from the wire along a line perpendicular to the wire.
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The number density of electrons in the aluminium metal is . Calculate the drift velocity of electrons in a aluminium wire of cross-sectional area
in which a current of 4 A is flowing.
What do you understand by linear conductors? Discuss the conditions under which metals do not behave as linear conductors.
See Answer →hree capacitors are connected to each other as shown below:
Calculate the equivalent capacitance between points A and B.
See Answer →State Gauss’s Law. What does spherically symmetric charge distribution mean? Use Gauss’s Law to determine the electric field of a solid metallic sphere of radius R having volume charge density at a point outside the sphere.
Two positively charged particles having charges and
, respectively, are kept at a distance of
from each other. Determine the force on each charge and the electric field due to each charge. Show the force and electric field vectors on appropriate diagrams. What is the resultant force at a point midway from the two charges along the straight line joining them?
Calculate the flux of a vector field through the surface of a cube defined by
.
Calculate the net work done by a force in taking a particle along the straight line between the points (5, -3) to (0,0) and then along the straight line between the points (0,0) to (5,3). Is the force conservative? Explain.
Consider a rigid body rotating about a fixed axis with a constant angular velocity , directed along the axis of rotation. The velocity
of a particle on the rigid body is
. Calculate
.
The height of a hill is given by . Calculate the maximum rate of change (also called the steepest ascent) in the height of the hill at the point (2,1). What is its direction?
What is Fermi-energy? Obtain an expression for Fermi energy for a system of N Fermions enclosed in a volume V. What will be the value of Fermi-energy (in eV) of gold at Fermi-temperature ?
Using the Planck's radiation law:
and (iii) Stefan's law. (10)
N particles obey MB distribution. They are distributed among three states with energies and
. If the equilibrium energy of the system is 2000 kBT, calculate the total number of particles, N.
Derive an expression of the partition function for a single particle monatomic ideal gas. Write the expression for a monatomic gas consisting of N-identical yet distinguishable and non-interacting particles.
See Answer →What is Joule-Thomson effect? Write any four findings of Joule- Thomson experiment.
See Answer →Derive Clausius-Clayperon equation of phase transition. Draw phase diagram of water.
See Answer →Using the Maxwell's relations of thermodynamics, obtain the first and second TdS-equations.
See Answer →Draw p-V diagram of the Carnot Cycle and hence obtain an expression of efficiency.
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