*Chapter 35, Problem 033 GO Three electromagnetic waves travel through a certain point P along an x axis. They are polarized parallel to a y axis, with the following variations in their amplitudes. Find their resultant at P. E1 = (3.0 x 105 V/m) sin[(3.0 x 1014 rad/s)t] Ez = (4.0 × 106 V/m) sin[(3.0 x 1014 rad/s)t + 45°] %3D (40 x 10-6 vim o14
*Chapter 35, Problem 033 GO Three electromagnetic waves travel through a certain point P along an x axis. They are polarized parallel to a y axis, with the following variations in their amplitudes. Find their resultant at P. E1 = (3.0 x 105 V/m) sin[(3.0 x 1014 rad/s)t] Ez = (4.0 × 106 V/m) sin[(3.0 x 1014 rad/s)t + 45°] %3D (40 x 10-6 vim o14
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![### Chapter 35, Problem 033 GO
Three electromagnetic waves travel through a certain point \( P \) along an x-axis. They are polarized parallel to a y-axis, with the following variations in their amplitudes. Find their resultant at \( P \).
\[ E_1 = (3.0 \times 10^{-5} \, \text{V/m}) \sin[(3.0 \times 10^{14} \, \text{rad/s})t] \]
\[ E_2 = (4.0 \times 10^{-6} \, \text{V/m}) \sin[(3.0 \times 10^{14} \, \text{rad/s})t + 45^\circ] \]
\[ E_3 = (4.0 \times 10^{-6} \, \text{V/m}) \sin[(3.0 \times 10^{14} \, \text{rad/s})t - 45^\circ] \]
The resultant electric field \( E \) at point \( P \) can be represented as:
\[ E = (\quad\quad\quad )^{*1} \]
\[ \quad\quad\quad (\quad\quad\quad ) \sin\left[ (\quad\quad\quad )^{*2} \times 10^{14} (\quad\quad\quad ) t + \quad \right]^{*3} \]
In this problem, your goal is to determine the final expression for the resultant electric field \( E \) by combining the individual waves \( E_1 \), \( E_2 \), and \( E_3 \).
---
**Explanation:**
To find the resultant field, you need to sum the individual fields vectorially. The electric fields \( E_2 \) and \( E_3 \) have additional phase angles of \( +45^\circ \) and \( -45^\circ \) respectively, which will necessitate using trigonometric identities for their combination with \( E_1 \). The final expression for \( E \) will involve determining the total amplitude and potential phase shifts.
This problem is an example of superposition of waves, which is a common phenomenon in the study of electromagnetic fields, optics, and wave physics. Understanding how to handle such combinations is critical for fields such as physics, electrical engineering, and applied mathematics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fffec9791-3e70-4062-ab52-19ffbcf6a19b%2F6a2d4e71-60ff-4f08-838a-1c6adc6cfafc%2Fr61sp569_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Chapter 35, Problem 033 GO
Three electromagnetic waves travel through a certain point \( P \) along an x-axis. They are polarized parallel to a y-axis, with the following variations in their amplitudes. Find their resultant at \( P \).
\[ E_1 = (3.0 \times 10^{-5} \, \text{V/m}) \sin[(3.0 \times 10^{14} \, \text{rad/s})t] \]
\[ E_2 = (4.0 \times 10^{-6} \, \text{V/m}) \sin[(3.0 \times 10^{14} \, \text{rad/s})t + 45^\circ] \]
\[ E_3 = (4.0 \times 10^{-6} \, \text{V/m}) \sin[(3.0 \times 10^{14} \, \text{rad/s})t - 45^\circ] \]
The resultant electric field \( E \) at point \( P \) can be represented as:
\[ E = (\quad\quad\quad )^{*1} \]
\[ \quad\quad\quad (\quad\quad\quad ) \sin\left[ (\quad\quad\quad )^{*2} \times 10^{14} (\quad\quad\quad ) t + \quad \right]^{*3} \]
In this problem, your goal is to determine the final expression for the resultant electric field \( E \) by combining the individual waves \( E_1 \), \( E_2 \), and \( E_3 \).
---
**Explanation:**
To find the resultant field, you need to sum the individual fields vectorially. The electric fields \( E_2 \) and \( E_3 \) have additional phase angles of \( +45^\circ \) and \( -45^\circ \) respectively, which will necessitate using trigonometric identities for their combination with \( E_1 \). The final expression for \( E \) will involve determining the total amplitude and potential phase shifts.
This problem is an example of superposition of waves, which is a common phenomenon in the study of electromagnetic fields, optics, and wave physics. Understanding how to handle such combinations is critical for fields such as physics, electrical engineering, and applied mathematics.
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