Question

problem 22.07
in an em wave traveling west, the b field oscillates up and down vertically and has a frequency of 92.0 khz and an rms strength of 7.45 × 10⁻⁹ t. assume that the wave travels in free space
what is the frequency of the electric field?
express your answer to three significant figures and include the appropriate units.

part b
what is the rms strength of the electric field?
express your answer to three significant figures and include the appropriate units.

Explanation:

Part A: Frequency of the electric field

Step1: Recall the property of EM waves

In an electromagnetic (EM) wave, the frequency of the electric field ($E$) is equal to the frequency of the magnetic field ($B$).

Step2: Convert the unit if necessary

Given the frequency of the $B$ - field $f = 92.0\ kHz$. Since $1\ kHz=10^{3}\ Hz$, but the value $92.0\ kHz$ already has three significant figures and we just need to state the frequency of the $E$ - field.

Part B: RMS strength of the electric field

Step1: Use the relationship between $E_{rms}$ and $B_{rms}$

The relationship between the rms value of the electric field ($E_{rms}$) and the rms value of the magnetic field ($B_{rms}$) in an EM wave is $E_{rms}=cB_{rms}$, where $c = 3\times10^{8}\ m/s$ (speed of light in free - space).

Step2: Substitute the values

Given $B_{rms}=7.45\times 10^{-9}\ T$. Then $E_{rms}=(3\times 10^{8}\ m/s)\times(7.45\times 10^{-9}\ T)$.

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Answer:

• Part A: $f = 92.0\ kHz$
• Part B: $E_{rms}=2.24\ V/m$