Question

A plane electromagnetic wave, has frequency of 2.0 × 10¹⁰ Hz and its energy density is 1.02 × 10^-8 J/m³ in vacuum. The amplitude of the magnetic field of the wave is close to `(1/(4piepsilon_0) = 9xx10^9"Nm"^2/"C"^2  "and speed of light" = 3 xx 10^8  "m"  "s"^-1)`:

Options

• 160 nT

• 180 nT

• 190 nT

• 150 nT

Answer 1

160 nT

Explanation:

Given: Frequency of electromagnetic wave is f = 2.0 × 10¹⁰ Hz, energy density of the wave is e = 1.02 × 10^-8 J/m³.

To find: B, the amplitude of magnetic field associated with the wave.

Energy density associated with an electromagnetic wave in vacuum:

ε = `1/2 "B"^2/mu_0`

B = `sqrt(2mu_0epsilon)`

B = `sqrt(2xx4pixx10^-7xx1.02xx10^-8)`

B = 160 nT