Question

The magnetic field in a plane electromagnetic wave travelling in glass (n = 1.5) is given by

B_y = (2 × 10⁻⁷ T) sin (αx + 1.5 × 10¹¹ t)

where x is in metres and t is in seconds. The value of α is ______.

Options

• 0.5 × 10³ m⁻¹

• 6.0 × 10² m⁻¹

• 7.5 × 10² m⁻¹

• 1.5 × 10³ m⁻¹

Answer 1

The magnetic field in a plane electromagnetic wave travelling in glass (n = 1.5) is given by

B_y = (2 × 10⁻⁷ T) sin (αx + 1.5 × 10¹¹ t)

where x is in metres and t is in seconds. The value of α is 7.5 × 10² m⁻¹.

Explanation:

A plane electromagnetic wave is represented as:

sin(kx ± ωt)

Where,

k = wave number = `omega/v`

ω = angular frequency

v = speed of wave in medium

From the wave equation:

ω = 1.5 × 10¹¹ rad/s

Refractive index (n) = 1.5

Speed of EM wave in medium:

v = `c/n`

= `(3 xx 10^8)/1.5`

= 2 × 10⁸ m/s

Wave number (k) = `omega/v`

= `(1.5 xx 10^11)/(2 xx 10^8)`

= 0.75 × 10³

= 7.5 × 10² m⁻¹

Comparing with sin(αx + ωt), we get:

α = k

= 7.5 × 10² m⁻¹