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 long, straight, horizontal wire carries current I toward the right. A rectangular loop of wire, with length L and height w, lies below the straight wire. The length is parallel to the straight wire, and the top edge of the loop is a distance h below the straight wire. (a) Determine the magnetic flux through the loop due to the current I. (Use any variable stated above along with the following as necessary: Ho-)
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 long, straight, horizontal wire carries current I toward the right. A rectangular loop of wire, with length L and height w, lies below the straight wire. The length is parallel to the straight wire, and the top edge of the loop is a distance h below the straight wire. (a) Determine the magnetic flux through the loop due to the current I. (Use any variable stated above along with the following as necessary: Ho-)
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A long, straight, horizontal wire carries current \( I \) toward the right. A rectangular loop of wire, with length \( L \) and height \( w \), lies below the straight wire. The length is parallel to the straight wire, and the top edge of the loop is a distance \( h \) below the straight wire.
**Questions:**
### (a) Magnetic Flux Calculation
Determine the magnetic flux through the loop due to the current \( I \). (Use any variable stated above along with the following as necessary: \( \mu_0 \)).
\[ \Phi_B = \text{______} \]
### (b) Electromotive Force (emf) Calculation
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 \( b = 20.0 \, \text{A/s} \), \( h = 1.00 \, \text{cm} \), \( w = 20.0 \, \text{cm} \), and \( L = 1.15 \, \text{m} \).
\[ \text{emf} = \text{______} \, \text{V} \]
### (c) Direction of the Induced Current
What is the direction of the induced current in the rectangle?
- [ ] clockwise
- [ ] counterclockwise
- [ ] The magnitude is zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d3b999f-40bc-4397-b918-1b796d12487f%2F7bfa197b-900b-4573-9ba5-894fd94e842b%2Fn56zdxr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Electromagnetic Induction with a Rectangular Loop and a Straight Wire
**Introduction:**
A loop of wire in the shape of a rectangle with width \( w \) and length \( L \), and a long, straight wire carrying a current \( I \) lie on a tabletop as shown in the figure below.
**Figure Details:**
- A long, straight, horizontal wire carries current \( I \) toward the right.
- A rectangular loop of wire, with length \( L \) and height \( w \), lies below the straight wire.
- The length \( L \) is parallel to the straight wire, and the top edge of the loop is a distance \( h \) below the straight wire.
A long, straight, horizontal wire carries current \( I \) toward the right. A rectangular loop of wire, with length \( L \) and height \( w \), lies below the straight wire. The length is parallel to the straight wire, and the top edge of the loop is a distance \( h \) below the straight wire.
**Questions:**
### (a) Magnetic Flux Calculation
Determine the magnetic flux through the loop due to the current \( I \). (Use any variable stated above along with the following as necessary: \( \mu_0 \)).
\[ \Phi_B = \text{______} \]
### (b) Electromotive Force (emf) Calculation
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 \( b = 20.0 \, \text{A/s} \), \( h = 1.00 \, \text{cm} \), \( w = 20.0 \, \text{cm} \), and \( L = 1.15 \, \text{m} \).
\[ \text{emf} = \text{______} \, \text{V} \]
### (c) Direction of the Induced Current
What is the direction of the induced current in the rectangle?
- [ ] clockwise
- [ ] counterclockwise
- [ ] The magnitude is zero.
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