The electric field of a plane EM wave travelling in a non-magnetic medium is given by:

E_y = 20 sin(3×10⁶x − 4.5×10¹⁴t) V/m

Find the dielectric constant of the medium.

Solution:

Compare with standard wave equation:

E = E₀ sin(kx − ωt)

So,

• Wave number, k = 3 × 10⁶ rad/m
• Angular frequency, ω = 4.5 × 10¹⁴ rad/s

Wave speed:

v = ω/k

v = (4.5 × 10¹⁴)/(3 × 10⁶)

v = 1.5 × 10⁸ m/s

For non-magnetic medium:

v = c/√ε_r

ε_r = (c/v)²

ε_r = (3 × 10⁸ / 1.5 × 10⁸)²

ε_r = 2²

ε_r = 4

Answer: 4