A charged particle (mass m and charge q)
moves along X-axis with velocity V₀. When it
passes through the origin it enters a region having uniform electric field
$$\overrightarrow E = - E\widehat j$$ which extends upto x = d.
Equation of path of electron in the region x > d is

A plane electromagnetic wave, has
frequency of 2.0 $$ \times $$ 10¹⁰ Hz and its energy density is 1.02 $$ \times $$ 10^–8 J/m³ in vacuum. The amplitude of the magnetic field of the wave is close to
( $${1 \over {4\pi {\varepsilon _0}}} = 9 \times {10^9}{{N{m^2}} \over {{C^2}}}$$ and speed of light
= 3 $$ \times $$ 10⁸ ms^–1)

A 5 $$\mu $$F capacitor is charged fully by a 220 V supply. It is then disconnected from the supply and is connected in series to another uncharged 2.5 $$\mu $$F capacitor. If the energy change during the charge redistribution is $${X \over {100}}J$$ then value of X to the nearest integer is _____.

A circular coil of radius 10 cm is placed in a uniform magnetic field of 3.0 $$ \times $$ 10^–5 T with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2 s. The maximum value of EMF induced (in $$\mu $$V) in the coil will be close to the integer _______.