JEE MainPhysicsElectromagnetic Waves
The electric field of an electromagnetic wave propagating in a vacuum is given by E = E₀ ( 1 2 i - 1 2 k ) ( t + ky) . The corresponding magnetic field vector B is :
Options
- AB = E₀ c (- 1 2 i - 1 2 k ) ( t + ky)
- BB = E₀ c ( 1 2 i + 1 2 k ) ( t + ky)
- CB = E₀ c ( 1 2 i + 1 2 k ) ( t + ky)
- DB = E₀ c ( 1 2 i - 1 2 k ) ( t - ky)
Correct answer
B. B = E₀ c ( 1 2 i + 1 2 k ) ( t + ky)
Step-by-step solution
From the phase term ( t + ky) , the wave is propagating in the -y direction. Thus, the unit vector along the direction of propagation is k _ prop = - j . The direction of the magnetic field is given by B = k _ prop E . B = (- j ) ( 1 2 i - 1 2 k ) B = - 1 2 ( j i ) + 1 2 ( j k ) Using j i = - k and j k = i , we get: B = - 1 2 (- k ) + 1 2 ( i ) = 1 2 i + 1 2 k The amplitude of the magnetic field is B₀ = E₀ c . Therefore, the complete magnetic field vector is: B = E₀ c ( 1 2 i + 1 2 k ) ( t + ky) Answer: B = E₀ c (