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Question:

The magnetic field of an electromagnetic wave is given by: B⃗ = 1.6 × 10^-6 cos (2 × 10^7 z + 6 × 10^15 t) (2î+ĵ) Wbm^2. The associated electric field will be :

E⃗ = 4.8 × 10^2 cos (2 × 10^7 z + 6 × 10^15 t) (î - 2 ĵ) Vm

E⃗ = 4.8 × 10^2 cos (2 × 10^7 z - 6 × 10^15 t) (2î + ĵ) Vm

E⃗ = 4.8 × 10^2 cos (2 × 10^7 z - 6 × 10^15 t) (-2ĵ + î) Vm

E⃗ = 4.8 × 10^2 cos (2 × 10^7 z + 6 × 10^15 t) (-î + 2 ĵ) Vm

Solution:

Correct option is A. E⃗ = 4.8 × 10^2 cos (2 × 10^7 z + 6 × 10^15 t) (î - 2 ĵ) Vm
If we use that direction of light propagation will be along E⃗×B⃗. Then (4) option is correct. Detailed solution is as following.
magnitude of E = CBE = 3 × 10^8 × 1.6 × 10^-6×√(5)
E = 4.8 × 10^2 √(5)
E⃗ and B⃗ are perpendicular to each other
⇒E⃗. B⃗ = 0
⇒ either direction of E⃗ is î - 2 ĵ or -î + 2 ĵ
from given option
Also wave propagation direction is parallel to
E⃗×B⃗ which is -k̂⇒E⃗ us along (-î + 2 ĵ)