The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by the expression E → x ,   y = 10 j ^ c o s 6 x + 8 z . The magnetic field B → x ,   z ,   t is given by ( c is the velocity of light.)

Step-by-step solution

E = E 0 cos ω t - K     → ·   r   → ∴ At any time t , K → = 6 i ^ + 8 k ^ B 0 = E 0 c = 10 c λ = 2 π k = 2 π 10 = π 5 Also, E → × B → = c → ∴ ω = 2 π f = 2 π c λ i ^ j ^ k ^ 0 1 0 B x B y B z = 6 i ^ + 8 k ^ 10 ω = 2 π × c π 5 = 10 c ∴ i ^ B z - 0 + j ^ 0 + k ^ - B x = 0.6 i ^ - 0.8 k ^ Comparing the coefficients on both sides, ∴ B z = 0.6 ;   B x = - 0.8 B