The four arms of a Wheatstone bridge have the following resistances: AB = 100\,\Omega, BC = 10\,\Omega, CD = 5\,\Omega, DA = 60\,\Omega A galvanometer of 15\,\Omega resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10 volts is maintained across AC.
Find whether the discharge of a condenser through the inductive circuit is oscillatory when C = 0.1\,\mu\mathrm{F}, L:=10\,\mathrm{mH} and R = 200\,\Omega. If it is oscillatory, calculate its frequency.
Find out the total electric potential energy of a single spherical object of uniform charge density \rho, total charge Q and radius R.
Using Maxwell's field equations for a homogeneous non-conducting medium, derive the wave equation for the electric field. Calculate the velocity of EM wave in free space.
Explain the term 'Poynting vector' and state the significance of Poynting theorem.
Calculate the skin depth for radio waves in free space of wavelength 3 m in copper, given that electrical conductivity for copper is 6\times10^{7}\,\Omega^{-1}\,\mathrm{m}^{-1}.
What happens if the primary winding of a transformer is connected to a battery?
Obtain Poisson's equation in electrostatics from Gauss' law. What form does it take when the charge density is zero?
A wire of length 2 m is perpendicular to X-Y plane. It is moved with a velocity \vec{V}=(2\hat{i}+3\hat{j}+\hat{k})\,\mathrm{ms}^{-1} through a region of uniform induction \vec{B}=(\hat{i}+2\hat{j})\mathrm{Wm}^{-2}. Compute the potential difference between the ends of the wire.
Calculate, giving necessary steps, the radio frequency at which nuclear magnetic resonance occurs in water kept in a uniform magnetic field of 2.4\ \mathrm{T}. The magnetic moment of proton is 2.793\mu_N.
A series circuit has an inductance of 200 microhenries, a capacitance of 0.0005 microfarad and a resistance of 10 ohms. Find the resonant frequency and quality factor of the circuit.
Discuss the growth of current when an e.m.f. is suddenly applied to a circuit containing resistance, inductance and capacitance in series. What is the time constant of the circuit?
What is meant by a dielectric? Define polarization vector P and relate it with the average molecular dipole moment. Obtain expression for the potential due to a polarized dielectric in terms of the polarization vector.
In a non-charged current-free dielectric, \rho = 0 and \vec{J} = 0. Show that in this medium, electric (\vec{E}) and magnetic (\vec{H}) fields satisfy three-dimensional wave equations \nabla^2 \vec{E} = \varepsilon\mu \frac{\partial^2 \vec{E}}{\partial t^2} \quad \text{and} \quad \nabla^2 \vec{H} = \varepsilon\mu \frac{\partial^2 \vec{H}}{\partial t^2} Using Poynting theorem of electromagnetic theory, describe the significance of the vector \vec{P} = (\vec{E} \times \vec{H}) and the scalar u = \frac{1}{2} [\vec{B} \cdot \vec{H} + \vec{D} \cdot \vec{E}]
A plane-polarised electromagnetic wave is incident on the interface of two dielectrics having dielectric permittivity \varepsilon_1 and \varepsilon_2. Assume that the electric vector \vec{E} lies in the plane of incidence. Using the boundary conditions at the interface, obtain the expressions for the amplitude reflection coefficient (r_{11}) and the amplitude transmission constant (t_{11}). Using the components of the Poynting vector \vec{E} \times \vec{H} associated with the reflected and transmitted waves, obtain the expressions for reflection and transmission coefficients R_{11} and T_{11} respectively. Under what condition, r_{11} = 0 and t_{11} = 1?
Consider the incidence of a plane-polarised electromagnetic wave at the interface of two media having dielectric permittivity and magnetic permeability (\varepsilon_1, \mu_1) and (\varepsilon_2, \mu_2) respectively. The interface is chosen to be x = 0 plane. \vec{K}_1, \vec{K}_2 and \vec{K}_3 represent the propagator vectors associated with the incident, refracted and reflected waves respectively. Using the boundary conditions on them, establish the Snell's laws of refraction.
State Biot-Savart law. Calculate the magnitude of axial magnetic induction due to a circular loop of area A carrying current I.
Consider in the region 0 \le z \le 1\text{ m} an infinite slab made of a material with relative permeability, \mu_r = 3\cdot 5. If \vec{B} = (2y\hat{i} - 5x\hat{j}) \times 10^{-3}\text{ Wb/m}^2 within the slab, determine magnetisation \vec{M}.
For an arbitrary localised charged distribution, obtain an expression of electrostatic potential V in terms of multipole expansion.
A long solenoid of radius R and n turns per unit length carries a sinusoidal current I = I_0 \cos \omega t. Determine the magnitude of induced electric field (E) outside the solenoid.