A varying current i(t) = t(16 – t) A (t in seconds) flows through a long straight wire that lies along the x-axis. The current produces a magnetic field B whose magnitude at a distance r from the wire is B = HT. Furthermore, at the point P, B point: away from the observer as shown in the figure. Wire loop C- Rectangular region R Volt meter x=0) P=(x, y) Calculate the flux (1), at time t, of B through a rectangle of dimensions L x H = 9 x 2 m whose top and bottom edges are parallel to the wire and whose bottom edge is located d = 0.5 m above the wire. Assume that the rectangle and the wire are
A varying current i(t) = t(16 – t) A (t in seconds) flows through a long straight wire that lies along the x-axis. The current produces a magnetic field B whose magnitude at a distance r from the wire is B = HT. Furthermore, at the point P, B point: away from the observer as shown in the figure. Wire loop C- Rectangular region R Volt meter x=0) P=(x, y) Calculate the flux (1), at time t, of B through a rectangle of dimensions L x H = 9 x 2 m whose top and bottom edges are parallel to the wire and whose bottom edge is located d = 0.5 m above the wire. Assume that the rectangle and the wire are
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![# Faraday's Law and Magnetic Flux Calculation
A varying current \( i(t) = t(16 - t) \, \text{A} \) (where \( t \) is in seconds) flows through a long straight wire lying along the x-axis. The current produces a magnetic field \( B \) whose magnitude at a distance \( r \) from the wire is given by:
\[
B = \frac{\mu_0 I}{2 \pi r} \, \text{T}
\]
At point \( P \), \( B \) points away from the observer as shown in the figure.
## Diagram Explanation
- **Wire Loop C**: Represents the path around which we are analyzing the magnetic field.
- **Rectangular Region \( R \)**: A wire loop described as a rectangle.
- **Dimensions**: The rectangle has dimensions \( L \times H = 9 \times 2 \, \text{m} \).
- **Positioning**: The bottom edge of the rectangle is located \( d = 0.5 \, \text{m} \) above the wire, in the same plane as the wire.
## Task
1. **Calculate the Flux \( \Phi(t) \)**:
- Determine \( \Phi(t) \), at time \( t \), through the rectangular area.
- Express in terms of symbolic notation using \( \mu_0 \) and \( I(t) \).
\[
\Phi(t) = \quad \underline{\hspace{10cm}} \quad \text{T} \cdot \text{m}^2
\]
2. **Determine Voltage Drop Using Faraday's Law**:
- Calculate the voltage drop around the rectangular loop at \( t = 6 \, \text{s} \).
- Use symbolic notation and assume \( \mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A} \).
\[
\oint_C \mathbf{E} \cdot d\mathbf{r} = \quad \underline{\hspace{10cm}} \quad \text{V}
\]
This setup helps in illustrating applications of Faraday's Law and the concepts of magnetic flux in electromagnetic theory.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77548912-c51c-4c9d-8b51-f3905a3bec75%2F84b5c970-39a3-4991-8b7b-4a61280658c9%2F975h4sv_processed.png&w=3840&q=75)
Transcribed Image Text:# Faraday's Law and Magnetic Flux Calculation
A varying current \( i(t) = t(16 - t) \, \text{A} \) (where \( t \) is in seconds) flows through a long straight wire lying along the x-axis. The current produces a magnetic field \( B \) whose magnitude at a distance \( r \) from the wire is given by:
\[
B = \frac{\mu_0 I}{2 \pi r} \, \text{T}
\]
At point \( P \), \( B \) points away from the observer as shown in the figure.
## Diagram Explanation
- **Wire Loop C**: Represents the path around which we are analyzing the magnetic field.
- **Rectangular Region \( R \)**: A wire loop described as a rectangle.
- **Dimensions**: The rectangle has dimensions \( L \times H = 9 \times 2 \, \text{m} \).
- **Positioning**: The bottom edge of the rectangle is located \( d = 0.5 \, \text{m} \) above the wire, in the same plane as the wire.
## Task
1. **Calculate the Flux \( \Phi(t) \)**:
- Determine \( \Phi(t) \), at time \( t \), through the rectangular area.
- Express in terms of symbolic notation using \( \mu_0 \) and \( I(t) \).
\[
\Phi(t) = \quad \underline{\hspace{10cm}} \quad \text{T} \cdot \text{m}^2
\]
2. **Determine Voltage Drop Using Faraday's Law**:
- Calculate the voltage drop around the rectangular loop at \( t = 6 \, \text{s} \).
- Use symbolic notation and assume \( \mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A} \).
\[
\oint_C \mathbf{E} \cdot d\mathbf{r} = \quad \underline{\hspace{10cm}} \quad \text{V}
\]
This setup helps in illustrating applications of Faraday's Law and the concepts of magnetic flux in electromagnetic theory.
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