A left circularly polarized light beam of wavelength 600 nm is incident on a crystal of thickness d and propagates perpendicular to its optic axis. The ordinary and extraordinary refractive indices of the crystal are no = 1.54 and ne and = 1.55 respectively. The emergent light will be right circularly polarized, if d is
A rod of length L with uniform charge density λ per unit length is in the XY-plane and rotating about Z-axis passing through one of its edge with an angular
velocity ω as shown in the figure below. (r^,ϕ^,z^) refer to the unit vectors at Q, A is the vector potential at a distance d from the origin O along Z-axis for d ≪ L and J is the current density due to the motion of the rod. Which one of the following statements is correct?
A dielectric sphere is placed in a uniform electric field directed along the positive Y-axis. Which one of the following represents the correct equipotential surfaces?
A copper wire of uniform cross-sectional area 1.0 × 0-6 m2 carries a current of 1 A. Assuming that each copper atom contributes one electron to the electron gas, the drift velocity of the free electrons (density of copper is 8.94 × 103 kg/m3 and its atomic mass is 1.05 × 10-25 kg) is
Four point charges are placed in a plane at the following positions +Q at (1, 0), -Q at (-1, 0), + Q at (0, 1) and -Q at (0, -1).
At large distances the electrostatic potential due to this charge distribution will be dominated by the
Three point charges q, q and -2q are located at (0, -a, a), (0, a, a) and (0, 0, -a), respectively. The net dipole moment of this charge distribution is
Consider the following three independent cases:
i. Particle A of charge +q moves in free space with a constant velocity v (v ≪ speed of light).
ii. Particle B of charge +q moves in free space in a circle of radius R with same speed v as In case i.
iii. Particle C having charge -q moves as in case ii.
If the powers radiated by A, B and C are PA, PB and PC respectively then
An infinitely long wire carrying a current I(t)=I0cos(ωt) is placed at a distance a from a square loop of side a as shown in the figure. If the resistance of the loop is R, then the amplitude of the induced current in the loop is
A large circular coil of N turns and radius R carries a time varying current I=I0sin(ωt). A small circular coil of n turns and radius r(r ≪ R) is placed at the centre of the large coil such that the coils are concentric and coplanar. The induced emf in the small coil
A conducting loop L of surface area S is moving with a velocity v in a magnetic field B(r,t)=B0t2,B0 is a positive constant of suitable dimensions. The emf
induced Vemf in the loop is given by
Unpolarized light falls from air to a planar air-glass interface (refractive index of glass is 1.5) and the reflected light is observed to be plane polarized. The polarization vector and the angle of incidence θi are
Consider the given statements about E(r, t) and B(r, t), the electric and magnetic vectors respectively in a region of free space
P. Both E and B are conservative vector fields.
Q. Both E and B are central force fields.
R. E and B are mutually perpendicular in the region.
S. Work done by B on a moving charge in the region is zero.
Choose the right combination of correct statements from the following.
An insulating sphere of radius a carries a charge density ρ(r)=ρ0(a2−r2)cosθ;r<a. The leading order term for the electric field at a distance d, far away from the charge distribution, is proportional to
At the interface between two linear dielectrics (with dielectric constants ε1 and ε2), the electric field lines bend, as shown in the figure. Assume that there are no free charges at the interface. The ratio ε2ε1 is
