The magnetic field of a plane electromagnetic wave is vector B = 3 x 10^-8 Sin[200π(y + ct)] T where c = 3 × 10^8 ms^–1 is the speed of light.

Question

The magnetic field of a plane electromagnetic wave is

 \(\vec{B}\) = 3 x 10^-8 Sin[200π(y + ct)] \(\hat{i}\)T 

where c = 3 × 10⁸ ms^–1 is the speed of light. The corresponding electric field is

(1) \(\vec{E}\) = -9 sin[200π(y + ct)]\(\hat{k}\) V/m

Answer 1

(1) \(\vec{E}\) = -9 sin[200π(y + ct)]\(\hat{k}\) V/m

 \(\vec{B}\) = 3 x 10^-8 sin[200π(y + ct)]\(\hat{i}\) T

⇒ Wave is trivelling along -y ditection with \(\vec{B}\) pointing along x-axis

E₀ = cB₀ = 9V/m

\(\vec{E}\) x \(\vec{B}\) gives direction of propagation of wave, so E must be along –z axis.

  \(\vec{E}\) = 9 sin[200π(y + ct)](-\(\hat{k}\)) V/m