Refer to diagram 3. A closed circular loop (N = 8,666 turns, radius r, resistance R = 4.19 Q) sits in a magnetic field B pointing perpendicular to the plane of the loop and into the page. This time: the magnitude of B is constant 3.85 T, but at t = 0 the radius of the loop dr begins to decrease at a steady rate, so = -0.512 cm/s. Assuming the total resistance of the loop does not change dt significantly, find I, the current induced in the loop at the instant r = 9.88 cm, in A. As before, give the answer as positive if the current is clockwise, and negative if the current is counter-clockwise.
Refer to diagram 3. A closed circular loop (N = 8,666 turns, radius r, resistance R = 4.19 Q) sits in a magnetic field B pointing perpendicular to the plane of the loop and into the page. This time: the magnitude of B is constant 3.85 T, but at t = 0 the radius of the loop dr begins to decrease at a steady rate, so = -0.512 cm/s. Assuming the total resistance of the loop does not change dt significantly, find I, the current induced in the loop at the instant r = 9.88 cm, in A. As before, give the answer as positive if the current is clockwise, and negative if the current is counter-clockwise.
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![**Educational Transcription:**
**Induced Current in a Closed Circular Loop**
In this scenario, we are looking at a closed circular loop with the following characteristics:
- Number of turns, \( N = 8,666 \)
- Radius, \( r \)
- Resistance, \( R = 4.19 \, \Omega \)
The loop is positioned in a magnetic field \( B \) that is pointing perpendicular to the plane of the loop and directed into the page.
Initially, the magnitude of the magnetic field \( B \) is constant at 3.85 T (Tesla). At time \( t = 0 \), the radius of the loop begins to decrease steadily, with the rate of change of the radius given by:
\[
\frac{dr}{dt} = -0.512 \, \text{cm/s}
\]
We assume that the total resistance of the loop does not change significantly during this process. The task is to find \( I \), the current induced in the loop, at the instant when the radius \( r = 9.88 \, \text{cm} \).
The current value should be provided in Amperes (A), with a positive sign indicating a clockwise current, and a negative sign indicating a counter-clockwise current.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2817b655-4143-4a03-afc5-4f301e3d6a93%2F597a2f68-65df-4a5d-a517-8e917ae8b73a%2Fz7ngunm_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Transcription:**
**Induced Current in a Closed Circular Loop**
In this scenario, we are looking at a closed circular loop with the following characteristics:
- Number of turns, \( N = 8,666 \)
- Radius, \( r \)
- Resistance, \( R = 4.19 \, \Omega \)
The loop is positioned in a magnetic field \( B \) that is pointing perpendicular to the plane of the loop and directed into the page.
Initially, the magnitude of the magnetic field \( B \) is constant at 3.85 T (Tesla). At time \( t = 0 \), the radius of the loop begins to decrease steadily, with the rate of change of the radius given by:
\[
\frac{dr}{dt} = -0.512 \, \text{cm/s}
\]
We assume that the total resistance of the loop does not change significantly during this process. The task is to find \( I \), the current induced in the loop, at the instant when the radius \( r = 9.88 \, \text{cm} \).
The current value should be provided in Amperes (A), with a positive sign indicating a clockwise current, and a negative sign indicating a counter-clockwise current.
Transcribed Image Text:**Diagram 3:**
The diagram consists of a circle at the center with the letter "X" inside it. Surrounding this circle are eight more "X" letters arranged in a 3x3 grid pattern, with the circle occupying the center position. The "X" letters are evenly distributed around the circle.
This configuration can illustrate concepts such as centrality in networks or positioning in spatial arrangements.
Expert Solution
Step 1
When a coil carrying current is placed in either a varying magnetic field or the coil itself is moving such that the area associated with the coil changes, then an emf is induced in the coil and it is given as-
where, is the flux associated with the coil
N is no. of turns in the coil
Flux is given as-
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