A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in the figure below. (a) Determine the magnetic flux through the loop due to the current I. (Use any variable stated above along with the following as necessary: Mo.) (b) Suppose the current is changing with time according to I = a + bt, where a and b are constants. Determine the magnitude of the emf (in V) that is induced in the loop if b = 20.0 A/s, h = 1.00 cm, w = 20.0 cm, and L = 1.15 m. (c) What is the direction of the induced current in the rectangle? clockwise counterclockwise The magnitude is zero.
A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in the figure below. (a) Determine the magnetic flux through the loop due to the current I. (Use any variable stated above along with the following as necessary: Mo.) (b) Suppose the current is changing with time according to I = a + bt, where a and b are constants. Determine the magnitude of the emf (in V) that is induced in the loop if b = 20.0 A/s, h = 1.00 cm, w = 20.0 cm, and L = 1.15 m. (c) What is the direction of the induced current in the rectangle? clockwise counterclockwise The magnitude is zero.
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![### Magnetic Flux Through a Wire Loop: Educational Exercise
#### Diagram
The diagram illustrates a loop of wire in the shape of a rectangle with width \(w\) and length \(L\). Above the rectangular loop lies a long, straight wire carrying a current \(I\). The distance between the wire and the rectangular loop is denoted as \(h\).
#### Exercise Questions
**(a) Determine the magnetic flux through the loop due to the current \(I\).**
(Use any variable stated above along with the following as necessary: \(\mu_0\))
\[\Phi_B = \quad \_\_\_\_\_\_ \]
**(b) Suppose the current is changing with time according to \(I = a + bt\), where \(a\) and \(b\) are constants. Determine the magnitude of the emf (in V) that is induced in the loop if \(b = 20.0 \, A/s\), \(h = 1.00 \, cm\), \(w = 20.0 \, cm\), and \(L = 1.15 \, m\).**
\[\_\_\_\_\_\_\_\_ \, V\]
**(c) What is the direction of the induced current in the rectangle?**
- ⬜ Clockwise
- ⬜ Counterclockwise
- ⬜ The magnitude is zero.
Please ensure students apply fundamental principles of electromagnetism, including Faraday's Law and the Biot-Savart Law, to solve these problems. They need to calculate the magnetic field due to a current-carrying wire and subsequently compute the induced emf using the rate of change of magnetic flux through the loop.
#### Diagram Explanation
The diagram features:
- A long, straight wire carrying a current \(I\) moving horizontally to the right.
- A rectangular loop of wire lying in the plane below the wire.
- Dimensions of the loop: width \(w\) and length \(L\).
- Distance from the wire to the loop, \(h\).
Students are expected to account for the magnetic field produced by the wire, which diminishes with distance from the wire, and understand how this influences the magnetic flux through the loop. The variation in time of the current also introduces an aspect of electromagnetic induction that students should recognize and calculate accordingly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d3b999f-40bc-4397-b918-1b796d12487f%2Fe2d71de4-d974-4e94-94cf-8d4e05ab2bfb%2Fni58a6u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Magnetic Flux Through a Wire Loop: Educational Exercise
#### Diagram
The diagram illustrates a loop of wire in the shape of a rectangle with width \(w\) and length \(L\). Above the rectangular loop lies a long, straight wire carrying a current \(I\). The distance between the wire and the rectangular loop is denoted as \(h\).
#### Exercise Questions
**(a) Determine the magnetic flux through the loop due to the current \(I\).**
(Use any variable stated above along with the following as necessary: \(\mu_0\))
\[\Phi_B = \quad \_\_\_\_\_\_ \]
**(b) Suppose the current is changing with time according to \(I = a + bt\), where \(a\) and \(b\) are constants. Determine the magnitude of the emf (in V) that is induced in the loop if \(b = 20.0 \, A/s\), \(h = 1.00 \, cm\), \(w = 20.0 \, cm\), and \(L = 1.15 \, m\).**
\[\_\_\_\_\_\_\_\_ \, V\]
**(c) What is the direction of the induced current in the rectangle?**
- ⬜ Clockwise
- ⬜ Counterclockwise
- ⬜ The magnitude is zero.
Please ensure students apply fundamental principles of electromagnetism, including Faraday's Law and the Biot-Savart Law, to solve these problems. They need to calculate the magnetic field due to a current-carrying wire and subsequently compute the induced emf using the rate of change of magnetic flux through the loop.
#### Diagram Explanation
The diagram features:
- A long, straight wire carrying a current \(I\) moving horizontally to the right.
- A rectangular loop of wire lying in the plane below the wire.
- Dimensions of the loop: width \(w\) and length \(L\).
- Distance from the wire to the loop, \(h\).
Students are expected to account for the magnetic field produced by the wire, which diminishes with distance from the wire, and understand how this influences the magnetic flux through the loop. The variation in time of the current also introduces an aspect of electromagnetic induction that students should recognize and calculate accordingly.
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