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. i (a) Determine the magnetic flux through the loop due to the current I. (Use any variable stated above along with the following as necessary: μ.) PB W (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 = 12.0 A/s, h = 1.00 cm, w = 15.0 cm, and L = 1.50 m. V (c) What is the direction of the induced current in the rectangle? O clockwise O counterclockwise O The magnitude is zero. What If? Suppose a constant current of I = 6.00 A flows in the straight wire and the loop moves from an initial position ho = 1.00 cm toward the bottom of the figure at a constant speed of v= 22.0 cm/s.
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. i (a) Determine the magnetic flux through the loop due to the current I. (Use any variable stated above along with the following as necessary: μ.) PB W (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 = 12.0 A/s, h = 1.00 cm, w = 15.0 cm, and L = 1.50 m. V (c) What is the direction of the induced current in the rectangle? O clockwise O counterclockwise O The magnitude is zero. What If? Suppose a constant current of I = 6.00 A flows in the straight wire and the loop moves from an initial position ho = 1.00 cm toward the bottom of the figure at a constant speed of v= 22.0 cm/s.
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Chapter1: Units, Trigonometry. And Vectors
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![### Magnetic Flux and Induced EMF in a Wire Loop
A loop of wire in the shape of a rectangle with width \( w \) and length \( L \) is positioned near a long, straight wire carrying a current \( I \) on a tabletop, as illustrated in the accompanying diagram.
#### Diagram Explanation:
- The diagram displays a rectangular loop with dimensions width \( w \) and length \( L \).
- A straight wire carrying a current \( I \) runs parallel to the length of the rectangle.
#### Problem Statements:
**(a)** Determine the magnetic flux \(\Phi_B\) through the loop due to the current \( I \). Use any variable stated above along with the necessary constant \(\mu_0\).
**Answer Box:**
\[ \Phi_B = \]
**(b)** If the current is changing with time according to \( I = a + bt \), where \( a \) and \( b \) are constants, determine the magnitude of the emf (in volts) induced in the loop given:
- \( b = 12.0 \, \text{A/s} \)
- \( h = 1.00 \, \text{cm} \)
- \( w = 15.0 \, \text{cm} \)
- \( L = 1.50 \, \text{m} \)
**Answer Box:**
\[ \text{EMF} = \]
**(c)** Determine the direction of the induced current in the rectangle:
- \( \circ \) clockwise
- \( \circ \) counterclockwise
- \( \circ \) The magnitude is zero.
---
**What If?**
Suppose a constant current of \( I = 6.00 \, \text{A} \) flows in the straight wire, and the loop moves from an initial position \( h_0 = 1.00 \, \text{cm} \) toward the bottom of the figure at a constant speed \( v = 22.0 \, \text{cm/s} \).
**(d)** What is the magnitude of the induced emf (in volts) in the loop 1.00 s after it begins to move?
**Answer Box:**
\[ \text{EMF} = \]
**(e)** Determine the direction of the induced current in the loop 1.00 s after it begins to move:
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e39d780-cdcb-4f47-bd02-8d33810f257b%2Fd1d11a78-cbc8-40a9-9830-e5eb42e51557%2Farea33n_processed.png&w=3840&q=75)
Transcribed Image Text:### Magnetic Flux and Induced EMF in a Wire Loop
A loop of wire in the shape of a rectangle with width \( w \) and length \( L \) is positioned near a long, straight wire carrying a current \( I \) on a tabletop, as illustrated in the accompanying diagram.
#### Diagram Explanation:
- The diagram displays a rectangular loop with dimensions width \( w \) and length \( L \).
- A straight wire carrying a current \( I \) runs parallel to the length of the rectangle.
#### Problem Statements:
**(a)** Determine the magnetic flux \(\Phi_B\) through the loop due to the current \( I \). Use any variable stated above along with the necessary constant \(\mu_0\).
**Answer Box:**
\[ \Phi_B = \]
**(b)** If the current is changing with time according to \( I = a + bt \), where \( a \) and \( b \) are constants, determine the magnitude of the emf (in volts) induced in the loop given:
- \( b = 12.0 \, \text{A/s} \)
- \( h = 1.00 \, \text{cm} \)
- \( w = 15.0 \, \text{cm} \)
- \( L = 1.50 \, \text{m} \)
**Answer Box:**
\[ \text{EMF} = \]
**(c)** Determine the direction of the induced current in the rectangle:
- \( \circ \) clockwise
- \( \circ \) counterclockwise
- \( \circ \) The magnitude is zero.
---
**What If?**
Suppose a constant current of \( I = 6.00 \, \text{A} \) flows in the straight wire, and the loop moves from an initial position \( h_0 = 1.00 \, \text{cm} \) toward the bottom of the figure at a constant speed \( v = 22.0 \, \text{cm/s} \).
**(d)** What is the magnitude of the induced emf (in volts) in the loop 1.00 s after it begins to move?
**Answer Box:**
\[ \text{EMF} = \]
**(e)** Determine the direction of the induced current in the loop 1.00 s after it begins to move:
-
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