The electric field associated with an electromagnetic wave travelling in vacuum is given by E_0 (3y + 4z + t)\, i , where is the angular frequency. All quantities are in SI units. The correct statement(s) about this wave is/are: [Given: speed of light in vacuum c = 3 10^8 ms^ -1 .]
C. The value of is 1.5 10^9 rad s^ -1 .
The given electric field is E = E_0 (3y + 4z + t)\, i . Comparing the phase = 3y + 4z + t with the standard wave equation phase k r - t, we can rewrite it as -(-3y - 4z - t). Thus, the wave vector is k = -3 j - 4 k . The direction of wave propagation is given by the unit vector n : n = k | k | = -3 j - 4 k (-3)^2 + (-4)^2 = - 1 5 (3 j + 4 k ) The magnitude of the wave vector is | k | = 5 m^ -1 . The angular frequency is: = c| k | = (3 10^8) 5 = 1.5 10^9 rad s^ -1 The magnetic field B is given by: B = 1 c ( n E ) = 1 c [ - 1 5 (3 j + 4 k ) ] [E_0 (3y + 4z + t)\, i ] B = - E_0 5c (3y + 4z + t) [3( j i ) + 4( k i )] B = - E_0 5c (3y + 4z + t) (-3 k + 4 j ) = E_0 5c (3y + 4z + t) (-4 j + 3 k ) Answer: The wave is travelling in - 1 5 (3 j + 4 k ) direction.; The value of is 1.5 10^9 rad s^ -1 .
Related: Physics — Electromagnetic Waves · All PYQ Banks