A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to

A sinusoidal voltage V(t) = 210 sin 3000 t volt is applied to a series LCR circuit in which L = 10 mH, C = 25 $$\mu$$F and R = 100 $$\Omega$$. The phase difference ($$\Phi $$) between the applied voltage and resultant current will be :

The electromagnetic waves travel in a medium at a speed of 2.0 $$\times$$ 10⁸ m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be :

The interference pattern is obtained with two coherent light sources of intensity ratio 4 : 1. And the ratio $${{{I_{\max }} + {I_{\min }}} \over {{I_{\max }} - {I_{\min }}}}$$ is $${5 \over x}$$. Then, the value of x will be equal to :