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(a) Calculate the frequency of the wave. MHZ (b) Calculate the magnetic field Bwhen the electric field has its maximum value in the negative y direction. magnitude direction -Select-- ]nT (c) Write an expression for Bwith the correct unit vector, with numerical values for Bmay k, and w, and with its magnitude in the form B = B cos (kx - wt).

(a) Calculate the frequency of the wave. MHZ (b) Calculate the magnetic field Bwhen the electric field has its maximum value in the negative y direction. magnitude direction -Select-- ]nT (c) Write an expression for Bwith the correct unit vector, with numerical values for Bmay k, and w, and with its magnitude in the form B = B cos (kx - wt).

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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.
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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