A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z-direction. At a particular point in space and time, the magnetic field is given by $$\overrightarrow B = 5 \times {10^{ - 8}}\widehat jT$$. The corresponding electric field $$\overrightarrow E $$ is (speed of light c = 3 × 10⁸ ms^–1)

In a double slit experiment, at a certain point on the screen the path difference between the two interfering waves is $${1 \over 8}$$th of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is :

As shown in figure, when a spherical cavity (centered at O) of radius 1 is cut out of a uniform sphere of radius R (centered at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e, on the surface of the cavity. R can be detemined by the equation :

The series combination of two batteries, both of the same emf 10 V, but different internal resistance of 20$$\Omega $$ and 5$$\Omega $$, is connected to the parallel combination of two resistors 30$$\Omega $$ and R $$\Omega $$. The voltage difference across the battery of internal resistance 20$$\Omega $$ is zero, the value of R (in $$\Omega $$) is : _______