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.
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.
What are the limitations of Rayleigh-Jeans law in explaining the spectrum of radiations from a blackbody? Explain how these limitations were overcome in Planck's radiation law. Deduce Wien's displacement law from Planck's radiation law.
Distinguish between positive and negative crystals in terms of double refraction. How are these crystals used to make quarter wave plates? Explain how the quarter wave plate is used in producing elliptically and circularly polarized light.
Discuss the intensity distribution in Fraunhofer diffraction pattern due to a single slit. Obtain conditions for maxima and minima of the intensity distribution. Show that the intensity of the first maxima is about 4.95\% of that of the principal maxima.
When the two waves of nearly equal frequencies interfere, then show that the number of beats produced per second is equal to the difference of their frequencies.
Explain the principle and working of He-Ne laser. What is the role of He gas? Why is it necessary to use narrow tube? How many longitudinal modes can be excited for an He-Ne laser in a cavity of length 30 cm and having half width of gain profile of laser material 2 \times 10^{-3}\,\mathrm{nm}? The emission wavelength is 6328\,\mathring{\mathrm{A}}.
What do you mean by spherical aberration of a lens? Show that if two plano-convex lenses are kept at a distance equal to the difference of their focal lengths, the spherical aberration would be minimum.
A plane transmission grating has 3000 lines in all, having width of 3\ \mathrm{mm}. What would be the angular separation in the first order spectrum of the two sodium lines of wavelengths 5890\mathring{\mathrm{A}} and 5896\mathring{\mathrm{A}}? Can they be seen distinctly?
A rod of length l_0 is kept at rest in x'\,y' plane of its rest frame making an angle \theta_0 with x' axis. What is the length and orientation of the rod in a laboratory frame (x,y) in which the rod moves to the right with velocity v?
(i) If a particle of mass m is in a central force field f(r)\hat{r}, then show that its path must be a plane curve, where \hat{r} is a unit vector in the direction of position vector \vec{r}.
(ii) A block of mass m having negligible dimension is sliding freely in x-direction with velocity \vec{v}=v\hat{\imath} as shown in the diagram.
What is its angular momentum \vec{L}_O about origin O and its angular momentum \vec{L}_A about the point A on y-axis?
A rod of length L has non-uniform linear mass density (mass per unit length) \lambda, which varies as \lambda=\lambda_0\left(\dfrac{S}{L}\right); where \lambda_0 is a constant and S is the distance from the end marked `O' (as shown in the figure). Find the centre of mass of the rod.
A water drop of radius 0.04\ \mathrm{mm} is falling through air. If the coefficient of viscosity for air is 1.8 \times 10^{-4} poise, find its terminal velocity. If 100 such drops coalesce, what will be the new terminal velocity?
Use Gauss's theorem to calculate the gravitational potential due to a solid sphere at a point outside the sphere. Calculate the amount of work required to send a body of mass m from the Earth's surface to a height R/2, where R is the radius of the Earth.
Two capillary tubes of lengths 2l and l with internal radii r and 2r respectively are connected in series. Water flows through them in streamline. If the pressure difference across the first capillary is P, find the pressure difference across the second one.
Given above is a circuit of self biased p-channel JFET. If the pinch off voltage is 5.0\ \mathrm{V} and V_{\mathrm{DS}} = 6.0\ \mathrm{V}, calculate the saturation current I_{\mathrm{DSS}}.
An amplifier in common-emitter configuration is shown in the above figure. If the current gain \beta=100 and the a.c. emitter resistance =25.0\,\Omega, determine the input impedance and the voltage gain of the amplifier:
Obtain the expression for penetration depth using London's equation of superconductivity and explain its significance.
In a semiconductor, the effective masses of an electron and a hole are 0.07\,m_0 and 0.4\,m_0, respectively, where m_0 is the free electron mass. Assuming that the average relaxation time for the hole is half of that for the electrons, calculate the mobility of the holes when the mobility of the electrons is 0.8\,\mathrm{m^2\,volt^{-1}\,s^{-1}}.
Consider the operational amplifier circuit given above: Given, R_1=10\,\mathrm{k}\Omega, R_2=150\,\mathrm{k}\Omega and the product of the open loop gain of the amplifier and its bandwidth =10^6\,\mathrm{Hz}. Determine the closed loop bandwidth of the amplifier.
