A sinusoidal electromagnetic wave is propagating in a vacuum in the +z-direction. Review | Constants If at a particular instant and at a certain point in space the electric field is in the +x-direction and has a magnitude of 3.80 V/m, what is the magnitude of the magnetic field of the wave at this same point in space and instant in time? VE ΑΣΦ ? 8 B= 1.1 107 Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining T
A sinusoidal electromagnetic wave is propagating in a vacuum in the +z-direction. Review | Constants If at a particular instant and at a certain point in space the electric field is in the +x-direction and has a magnitude of 3.80 V/m, what is the magnitude of the magnetic field of the wave at this same point in space and instant in time? VE ΑΣΦ ? 8 B= 1.1 107 Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining T
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![### Problem Statement:
A sinusoidal electromagnetic wave is propagating in a vacuum in the +z-direction.
**Question:**
If at a particular instant and at a certain point in space the electric field is in the +x-direction and has a magnitude of 3.80 V/m, what is the magnitude of the magnetic field of the wave at this same point in space and instant in time?
### Answer Submission Interface:
- Input Box: A text box is provided for entering the value of the magnetic field \( B \).
- Current Input: \( B = 1.1 \times 10^{-8} \) T
- Submit Button: A button to submit your answer.
- Feedback: After submission, an incorrect message is displayed with the note:
- "Incorrect; Try Again; 4 attempts remaining."
**Explanation for Incorrect Answer:**
The provided value \( 1.1 \times 10^{-8} \) T is flagged as incorrect. To solve for the correct magnetic field, use the relationship between the electric field \( \mathbf{E} \) and the magnetic field \( \mathbf{B} \) in an electromagnetic wave propagating in a vacuum:
\[ c = \frac{E}{B} \]
Where:
- \( c \) is the speed of light in a vacuum (\( c \approx 3.00 \times 10^8 \) m/s).
- \( E \) is the magnitude of the electric field.
- \( B \) is the magnitude of the magnetic field.
Given:
- \( E = 3.80 \) V/m
Rearranging the formula to solve for \( B \):
\[ B = \frac{E}{c} = \frac{3.80 \text{ V/m}}{3.00 \times 10^8 \text{ m/s}} \approx 1.27 \times 10^{-8} \text{ T} \]
### Correct Answer:
\[ B \approx 1.27 \times 10^{-8} \text{ T} \]
To correctly solve the problem and avoid incorrect submissions, understanding this relationship and careful calculation are crucial.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d4f1709-330a-4d41-ae4f-aad2db91bb03%2F0eb4a136-56fd-4bbe-84a9-cd0b9f7d1b91%2Fudsdlo_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
A sinusoidal electromagnetic wave is propagating in a vacuum in the +z-direction.
**Question:**
If at a particular instant and at a certain point in space the electric field is in the +x-direction and has a magnitude of 3.80 V/m, what is the magnitude of the magnetic field of the wave at this same point in space and instant in time?
### Answer Submission Interface:
- Input Box: A text box is provided for entering the value of the magnetic field \( B \).
- Current Input: \( B = 1.1 \times 10^{-8} \) T
- Submit Button: A button to submit your answer.
- Feedback: After submission, an incorrect message is displayed with the note:
- "Incorrect; Try Again; 4 attempts remaining."
**Explanation for Incorrect Answer:**
The provided value \( 1.1 \times 10^{-8} \) T is flagged as incorrect. To solve for the correct magnetic field, use the relationship between the electric field \( \mathbf{E} \) and the magnetic field \( \mathbf{B} \) in an electromagnetic wave propagating in a vacuum:
\[ c = \frac{E}{B} \]
Where:
- \( c \) is the speed of light in a vacuum (\( c \approx 3.00 \times 10^8 \) m/s).
- \( E \) is the magnitude of the electric field.
- \( B \) is the magnitude of the magnetic field.
Given:
- \( E = 3.80 \) V/m
Rearranging the formula to solve for \( B \):
\[ B = \frac{E}{c} = \frac{3.80 \text{ V/m}}{3.00 \times 10^8 \text{ m/s}} \approx 1.27 \times 10^{-8} \text{ T} \]
### Correct Answer:
\[ B \approx 1.27 \times 10^{-8} \text{ T} \]
To correctly solve the problem and avoid incorrect submissions, understanding this relationship and careful calculation are crucial.
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