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![**Electromagnetic Waves: Understanding Wave Propagation**
**Figure Description**
The figure illustrates a plane electromagnetic sinusoidal wave propagating in the x-direction. Key features of the wave include:
- **Wavelength**: 48.0 m
- **Electric Field Amplitude**: 20.0 V/m, vibrating in the xy-plane
The direction of wave propagation is along the x-axis, with the electric field (\(\vec{E}\)) and magnetic field (\(\vec{B}\)) oriented perpendicular to each other and the direction of wave propagation.
**Problems and Calculation Steps**
(a) **Calculate the Frequency of the Wave**
- Given: Wavelength = 48.0 m
(b) **Calculate the Magnetic Field \(\vec{B}\) when the Electric Field has its Maximum Value in the Negative y-direction**
- **Magnitude**: \( \_\_\_\_ \) nT
- **Direction**: Select from options
(c) **Write an Expression for \(\vec{B}\) with the Correct Unit Vector**
- Expression format:
\[
B = B_{\text{max}} \cos(kx - \omega t)
\]
- Assume:
- \(B\) is in nT
- \(x\) is in meters
- \(t\) is in nanoseconds (n.s.)
**Expression for \(\vec{B}\)**:
\[
\vec{B} = -\_\_\_\_ \cos\left(\_\_\_\_ \times 10^7\right) \hat{k} \text{ nT}
\]
**Instructions for Completing the Tasks:**
- Fill in the blanks with appropriate values and units as per the given data.
- Use the properties of electromagnetic waves to determine unknown values such as frequency, using known relationships like \( c = \lambda \times f \), where \( c \) is the speed of light.](https://content.bartleby.com/qna-images/question/5b404284-f3ac-4fad-97e0-0e40daa06506/5a59de93-e88e-4f20-a173-1882fdea1c01/beu5h4_processed.png)
Transcribed Image Text:**Electromagnetic Waves: Understanding Wave Propagation**
**Figure Description**
The figure illustrates a plane electromagnetic sinusoidal wave propagating in the x-direction. Key features of the wave include:
- **Wavelength**: 48.0 m
- **Electric Field Amplitude**: 20.0 V/m, vibrating in the xy-plane
The direction of wave propagation is along the x-axis, with the electric field (\(\vec{E}\)) and magnetic field (\(\vec{B}\)) oriented perpendicular to each other and the direction of wave propagation.
**Problems and Calculation Steps**
(a) **Calculate the Frequency of the Wave**
- Given: Wavelength = 48.0 m
(b) **Calculate the Magnetic Field \(\vec{B}\) when the Electric Field has its Maximum Value in the Negative y-direction**
- **Magnitude**: \( \_\_\_\_ \) nT
- **Direction**: Select from options
(c) **Write an Expression for \(\vec{B}\) with the Correct Unit Vector**
- Expression format:
\[
B = B_{\text{max}} \cos(kx - \omega t)
\]
- Assume:
- \(B\) is in nT
- \(x\) is in meters
- \(t\) is in nanoseconds (n.s.)
**Expression for \(\vec{B}\)**:
\[
\vec{B} = -\_\_\_\_ \cos\left(\_\_\_\_ \times 10^7\right) \hat{k} \text{ nT}
\]
**Instructions for Completing the Tasks:**
- Fill in the blanks with appropriate values and units as per the given data.
- Use the properties of electromagnetic waves to determine unknown values such as frequency, using known relationships like \( c = \lambda \times f \), where \( c \) is the speed of light.
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