PYQ Bank

Assume \vec{E}=0 inside a perfect conductor. Elaborate on any other four electrostatic properties that arise from this property.

Explain the term 'mutual inductance' between two coils carrying current. Describe a method of determining mutual inductance between two coils of wire with relevant theory.

If considered a blackbody as a radiation-filled cavity at a uniform temperature T, demonstrate with an appropriate figure the electromagnetic wave patterns inside the cavity of length L for wavelengths \lambda = L, \frac{3}{2} L and 2L.

How do you justify the statement : "A current carrying conductor, although has no net charge experiences a force when placed in a magnetic field."

Find out the number of photons in a cavity of volume 1\cdot 00\text{ cm}^3 under thermal equilibrium at temperature T = 1000\ ^\circ\text{K}. Assume that \int_0^\infty \frac{x^2 dx}{e^x - 1} = 2\cdot 405.

The volume between two concentric conducting spherical surfaces of radii a and b (a<b) is filled with an inhomogeneous dielectric with \epsilon=\epsilon_0/(1+cr), where c is a constant and r is the radial coordinate. A charge +Q is placed on the inner surface, while the outer surface is grounded. Determine-

(i) \vec{D} in the region a<r<b;

(ii) capacitance of the device;

(iii) polarization charge density in the region a<r<b;

(iv) surface polarization charge densities at r=a and r=b.

Two lenses of focal lengths 8\text{ cm} and 4\text{ cm} are placed at a certain distance apart. Calculate the distance between the lenses if they form an achromatic combination.

A diffraction grating of width 5 cm with slits of width 10^{-4} cm separated by a distance of 2\times10^{-4} cm is illuminated by light of wavelength 550 nm. What will be the width of the principal maximum in the diffraction pattern? Would there be any missing orders?

The separation between the slits is 0.5\,\text{mm} in Young's double-slit experiment. The interference pattern observed on a screen placed 5\,\text{m} away reveals the location of the first maximum which is 6\,\text{mm} from the centre of the pattern. Calculate the wavelength of light and separation between second and third bright fringes.

Use matrix method to obtain an expression for the focal length of a coaxial combination of two thin lenses having focal lengths f_1 and f_2 separated by distance d.

The motion of a damped mechanical oscillator is represented by m\ddot{x}+\alpha\dot{x}+\beta x=0 where m, \alpha and \beta are constants. The oscillator is critically damped. The system is given an impulse at x=0 and t=0, resulting in an initial velocity v. After how much time the system experiences maximum displacement?

Show that a travelling wave on the string, clamped on both the ends, undergoes a phase change of \pi. Hence obtain the time-independent form of the wave equation representing a standing wave on the string.

Explain mathematically the phenomenon of beats. How does it differ from that of interference ?

When two tuning forks were sounded together, 24 beats were produced in 6\text{ seconds}. After loading one tuning fork with wax, they produced 30 beats in 6\text{ seconds}. If the unloaded fork frequency is 512, what is the frequency of the other ?

A body describing simple harmonic motion (SHM) has a maximum acceleration of 8\ \pi\text{m/sec}^2 and a maximum speed of 1\cdot 6\text{ m/sec}. Find the time period (T) and the amplitude (A) of SHM.

Derive an expression for intermodal dispersion for a multimodal step-index fibre.

A pulse of \lambda_0=600\,\mathrm{nm} and \Delta\lambda=10\,\mathrm{nm} propagates through a fibre which has a material dispersion coefficient of 50\,\mathrm{ps} per km per nm at 600\,\mathrm{nm}. Calculate the pulse broadening in traversing a 10\,\mathrm{km} length of the fibre. If the pulse width at the input of the fibre is 12\,\mathrm{ns}, what will be the pulse width at the output of the fibre?

Calculate the minimum thickness of a quartz plate which would behave as a quarter-wave plate for wavelength of light, \lambda=6000\,\mathring{\mathrm{A}}. The refractive indices for ordinary and extraordinary rays are \mu_o=1.544 and \mu_e=1.553.

A step-index silica fiber consists of core of refractive index 1\cdot 450 and diameter 90\ \mu\text{m}. If the numerical aperture of the fiber is 0\cdot 16, calculate : (i) the acceptance angle of the fiber, (ii) refractive index of the cladding, and (iii) if the fiber is immersed in water of refractive index 1\cdot 33, how does the acceptance angle change ?

An optical waveguide has core and cladding of refractive indices 1\cdot 46 and 1\cdot 45 respectively. (i) Calculate the maximum number of modes with wavelength \lambda = 900\text{ nm} that can travel if it is a planar waveguide of core thickness 10\ \mu\text{m}. (ii) What is the number of modes if it is a cylindrical fiber of diameter 10\ \mu\text{m} ?