The electric field of a plane electromagnetic wave propagating along the x direction in vacuum is $$\overrightarrow{E}=E_0\hat{j}\cos \left(\omega t-kx\right)$$. The magnetic field $$\overrightarrow{B}$$ , at the moment t = 0 is :

In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by $$\hat{k}$$ and $$2\hat{i}-2\hat{j}$$, respectively. What is the unit vector along direction of propagation of the wave?

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 plane electromagnetic wave is propagating along the direction {{\widehat i + \widehat j} \over {\sqrt 2 }} , with its polarization along the direction $$\hat{k}$$ . The correct form of the magnetic field of the wave would be (here B0 is an appropriate constant) :

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

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 $$\overrightarrow{B}=5\times 10^{-8}\hat{j}T$$. The corresponding electric field $$\overrightarrow{E}$$ is (speed of light c = 3 × 108 ms–1)

The electric field of a plane electromagnetic wave is given by \overrightarrow E = {E_0}{{\widehat i + \widehat j} \over {\sqrt 2 }}\cos \left( {kz + \omega t} \right) At t = 0, a positively charged particle is at the point (x, y, z) = \left( {0,0,{\pi \over k}} \right). If its instantaneous velocity at (t = 0) is $$v_0\hat{k}$$ , the force acting on it due to the wave is :

If the magnetic field in a plane electromagnetic wave is given by $$\overrightarrow{B}$$ = 3 $$\times$$ 10-8 sin(1.6 $$\times$$ 103x + 48 $$\times$$ 1010t)$$\hat{j}$$ T, then what will be expression for electric field ?

The magnetic field of a plane electromagnetic wave is $$\overrightarrow{B}=3\times 10^{-8}\sin \left[200\pi \left(y+ct\right)\right]\hat{i}$$ T where c = 3 $$\times$$ 108 ms–1 is the speed of light. The corresponding electric field is :

If the potential energy between two molecules is given by U = - {A \over {{r^6}}} + {B \over {{r^{12}}}}, then at equilibrium, separation between molecules, and the potential energy are :

A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale) :

Consider a force $$\overrightarrow{F}=-x\hat{i}+y\hat{j}$$ . The work done by this force in moving a particle from point A(1, 0) to B(0, 1) along the line segment is : (all quantities are in SI units)

An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg, The mass of the elevator itself is 920 kg and it moves with a constant speed of 3 m/s. The frictional force opposing the motion is 6000 N. If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator (g = 10 m/s2) must be at least :

A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to : (1 HP = 746 W, g = 10 ms-2)

An AC circuit has R= 100 $$\Omega$$, C = 2 $$\mu$$F and L = 80 mH, connected in series. The quality factor of the circuit is :

A series L-R circuit is connected to a battery of emf V. If the circuit is switched on at t = 0, then the time at which the energy stored in the inductor reaches \left( {{1 \over n}} \right) times of its maximum value, is :

A 750 Hz, 20 V (rms) source is connected to a resistance of 100 $$\Omega$$, an inductance of 0.1803 H and a capacitance of 10 $$\mu$$F all in series. The time in which the resistance (heat capacity 2 J/oC) will get heated by 10oC. (assume no loss of heat to the surroudnings) is close to :

In LC circuit the inductance L = 40 mH and capacitance C = 100 $$\mu$$F. If a voltage V(t) = 10sin(314t) is applied to the circuit, the current in the circuit is given as :

A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be: