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A plane electromagnetic wave, has frequency of 2.0 × 10^{10} Hz and its energy density is 1.02 × 10^{-8} J/m^{3} 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

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#### Solution

**160 nT**

**Explanation:**

**Given:** Frequency of electromagnetic wave is f = 2.0 × 10^{10} Hz, energy density of the wave is e = 1.02 × 10^{-8} J/m^{3}.

**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

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