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Define a plane electromagnetic wave. A plane polarized wave is incident on the interface between two dielectric media. Obtain expressions for the amplitudes of the reflected and transmitted waves when the incident wave is polarized with its electric field B vector perpendicular to the plane of incidence. Discuss the phase relationships of the reflected and transmitted waves with respect to the incident wave.
Two resistors of 600~\Omega and 800~\Omega are connected in series with a 7\text{ volts} battery. An ammeter of 10~\Omega resistance is used to measure current.
(i) What will be the reading in the ammeter?
(ii) Similarly if a voltmeter of 10000~\Omega resistance is used to measure the potential difference across the 600~\Omega resistor, what will be the reading in the voltmeter?
There is a potential gradient of 100\text{ V/m} normal to the surface of the earth. Assuming the earth to be a charged sphere of radius 6370\text{ km}, find the total charge on the earth.
(i) The equation for an alternating current is I = 42\cdot 42 \sin (314t). Find the following : Maximum value of current, Frequency, RMS value and Average value
(ii) A condenser of capacity 1~\mu\text{F} is first charged and then discharged through a resistance of 1\text{ M}\Omega. Calculate the time in which the charge on the condenser will fall to 50\% of its initial value.
(iii) Consider the displacement vector \vec{D}, given by \vec{D} = (10xyz^2 + 4x)\hat{i} + (5x^2 z^2)\hat{j} + (10x^2 yz)\hat{k}\text{ nC/m}^2 Find the total charge enclosed in a cube of volume 10^{-9}\text{ m}^3 located at the point (1, 2, 3).
State and explain Biot-Savart law. Obtain an expression for the magnetic field at the center of a circular loop of radius r metres, carrying a current of I amperes.
Two solenoids have 500 and 800 turns of wire and are placed co-axially close to each other. A current of 5.0 A in the first solenoid produces an average flux of 200\mu\mathrm{Wb} through its each turn and a flux of 100\mu\mathrm{Wb} through each turn of the second solenoid. Find the self-inductance of the first solenoid and the mutual inductance of the solenoids.
A 12.0 V battery is connected at t=0 to a series combination of a resistor R=10.0\Omega and an inductor L=5.0\mathrm{H}. At what rate is energy being stored in the inductor when the current in the circuit is 0.4 A?
A 0.5\,\mathrm{m} long cylindrical medium between two conducting plates has uniform charge density of 100\,\mathrm{nC/m^3}. The axis of the cylindrical medium is along z-axis. The left plate is at z=0 and has a potential of 10\,\mathrm{kV} and the right plate is grounded. Determine the electric field at axial distance z=0.2\,\mathrm{m}.
A current carrying circular wire loop of radius 1.0 cm has a magnetic moment 2.0\,\mathrm{mJ/T}. Determine the magnetic field at an axial distance of 3.0 cm from the centre of the loop.
A uniformly magnetized sphere of radius R has magnetization \vec{M}=M_0\hat{z}. If the scalar magnetic potentials inside and outside the sphere are given as under \phi_m=\frac{M_0}{3}z;\ r\leq R and \phi_m=\frac{M_0R^3}{3r^2}\cos\theta;\ r>R where, r,\theta are two spherical coordinates, find the magnetic field inside and outside the sphere.
In free space, the electric field of electromagnetic wave is given by \vec{E}(x, t) = 100 \cos (\omega t - kx) \hat{y}\text{ volt/metre} Find the average power crossing a circular area of radius 2\text{ metres} in the yz-plane.
Write down Maxwell's equations in integral form. Explain the significance of each of these equations.
A parallel plate capacitor has plate area =4.0\ \mathrm{cm^2} and plate separation =2.0\ \mathrm{mm}. An a.c. voltage V=20\sin(5\times10^{3}t) volts is applied across the plates. If the dielectric constant of the medium between the plates is \varepsilon_r=2.0, calculate the displacement current.
Construct the Hamiltonian of a charged particle with charge q and mass m moving with the velocity \vec{v} in the external electromagnetic field, \vec{E}=E_0 \hat{i}, \vec{B}=B_0 \hat{k}, where E_0 and B_0 are constants.
(i) Show that the electric and magnetic energy densities in a plane travelling wave are equal. Also prove that the total energy density = \varepsilon_0 E^2 = \mu_0 H^2.
(ii) Deduce the equation of continuity based on Maxwell's equations.
Write down the physical significance of Maxwell's equations and explain the concept of displacement current by using a proper example.
Write down the four Maxwell's equations and explain the contribution of Maxwell in the development of these equations.
Write down the electromagnetic wave equations in non-conducting dielectric medium. Hence show that the velocity of wave propagation is given by v=\sqrt{\frac{1}{\varepsilon\mu}}, where the symbols have their usual meanings.
(i) Using Maxwell's equations, obtain the relation \frac{1}{c} \frac{\partial}{\partial t} \left( \frac{E^2 + B^2}{2} \right) + \vec{\nabla} \cdot (\vec{E} \times \vec{B}) = 0 (ii) What is Poynting vector ? Deduce Poynting theorem for the flow of energy in an electromagnetic field.
Discuss the reflection and refraction of plane electromagnetic waves at plane dielectric boundaries for normal incidence and also find the reflection and transmission coefficients.