The electric fields of two plane electromagnetic plane waves in vacuum are given by
$$\overrightarrow {{E_1}} = {E_0}\widehat j\cos \left( {\omega t - kx} \right)$$ and
$$\overrightarrow {{E_2}} = {E_0}\widehat k\cos \left( {\omega t - ky} \right)$$
At t = 0, a particle of charge q is at origin with
a velocity $$\overrightarrow v = 0.8c\widehat j$$ (c is the speed of light in vacuum). The instantaneous force experienced by the particle is :

Radiation, with wavelength 6561 $$\mathop A\limits^o $$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of 3 × 10^–4 T. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :

A particle moving with kinetic energy E has de Broglie wavelength $$\lambda $$. If energy $$\Delta $$E is added to its energy, the wavelength become $$\lambda $$/2. Value of $$\Delta $$E, is :

The aperture diameter of a telescope is 5m. The separation between the moon and the earth is 4 × 10⁵ km. With light of wavelength of 5500 $$\mathop A\limits^o $$, the minimum separation between objects on the surface of moon, so that they are just resolved, is close to :