B (T) A coil of wire has 25 turns and has a side length of 0.5 m. 0.80 square The coil is located in a variable magnetic field whose behavior is shown on the graph. At all times, the magnetic field is directed at an angle of 75° relative to the plane of the loops. What is the magnitude of the average emf induced in the coil in the time inter- val from t = 5.00 s to 7.50 s? 0.60 0.40 0.20 0.00 t (s) +00'01 f00's fos
B (T) A coil of wire has 25 turns and has a side length of 0.5 m. 0.80 square The coil is located in a variable magnetic field whose behavior is shown on the graph. At all times, the magnetic field is directed at an angle of 75° relative to the plane of the loops. What is the magnitude of the average emf induced in the coil in the time inter- val from t = 5.00 s to 7.50 s? 0.60 0.40 0.20 0.00 t (s) +00'01 f00's fos
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![### Transcription and Explanation for Educational Website
**Physics Problem Description**
A square coil of wire has 25 turns and has a side length of 0.5 m. The coil is located in a variable magnetic field whose behavior is shown on the graph. At all times, the magnetic field is directed at an angle of 75° relative to the plane of the loops. What is the magnitude of the average emf induced in the coil in the time interval from t = 5.00 s to 7.50 s?
**Graph Description**
The graph plots magnetic field strength \( B \) (measured in Tesla, T) against time \( t \) (measured in seconds, s).
**Detailed Graph Analysis:**
- The horizontal axis represents time \( t \) in seconds, ranging from 0.00 s to 10.00 s.
- The vertical axis represents magnetic flux density \( B \) in Tesla, ranging from 0.00 T to 0.80 T.
**Graph Observations:**
1. From \( t = 0 \) to \( t = 2.50 \) s, \( B \) increases linearly from 0.00 T to 0.20 T.
2. From \( t = 2.50 \) s to \( t = 5.00 \) s, \( B \) remains constant at 0.20 T.
3. From \( t = 5.00 \) s to \( t = 7.50 \) s, \( B \) increases linearly from 0.20 T to 0.80 T.
4. From \( t = 7.50 \) s to \( t = 10.00 \) s, \( B \) decreases linearly from 0.80 T to 0.20 T.
### Analyzing the Induced emf
To solve this problem, we need to use Faraday’s law of electromagnetic induction, which states that the induced emf (ε) in a coil is equal to the negative rate of change of magnetic flux through the coil:
\[ \epsilon = -N \frac{d\Phi}{dt} \]
Where:
- \( N \) is the number of turns in the coil.
- \( \Phi \) is the magnetic flux, calculated as \( \Phi = B \cdot A \cdot \cos(\theta) \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F81959cbb-8a2b-4bfe-a659-44f9c8ce4639%2Fc34607a0-fc85-4657-8681-6e7b08855522%2F8strqzi_processed.png&w=3840&q=75)
Transcribed Image Text:### Transcription and Explanation for Educational Website
**Physics Problem Description**
A square coil of wire has 25 turns and has a side length of 0.5 m. The coil is located in a variable magnetic field whose behavior is shown on the graph. At all times, the magnetic field is directed at an angle of 75° relative to the plane of the loops. What is the magnitude of the average emf induced in the coil in the time interval from t = 5.00 s to 7.50 s?
**Graph Description**
The graph plots magnetic field strength \( B \) (measured in Tesla, T) against time \( t \) (measured in seconds, s).
**Detailed Graph Analysis:**
- The horizontal axis represents time \( t \) in seconds, ranging from 0.00 s to 10.00 s.
- The vertical axis represents magnetic flux density \( B \) in Tesla, ranging from 0.00 T to 0.80 T.
**Graph Observations:**
1. From \( t = 0 \) to \( t = 2.50 \) s, \( B \) increases linearly from 0.00 T to 0.20 T.
2. From \( t = 2.50 \) s to \( t = 5.00 \) s, \( B \) remains constant at 0.20 T.
3. From \( t = 5.00 \) s to \( t = 7.50 \) s, \( B \) increases linearly from 0.20 T to 0.80 T.
4. From \( t = 7.50 \) s to \( t = 10.00 \) s, \( B \) decreases linearly from 0.80 T to 0.20 T.
### Analyzing the Induced emf
To solve this problem, we need to use Faraday’s law of electromagnetic induction, which states that the induced emf (ε) in a coil is equal to the negative rate of change of magnetic flux through the coil:
\[ \epsilon = -N \frac{d\Phi}{dt} \]
Where:
- \( N \) is the number of turns in the coil.
- \( \Phi \) is the magnetic flux, calculated as \( \Phi = B \cdot A \cdot \cos(\theta) \)
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