A rectangular, 13-turn planar wire loop has a resistance of 0.13 Q and an area of 2.26 m². A magnetic field perpendicular to the plane's loop increases steadily from 54 mT to 203 mT in 1.75 s. Calculate the magnitude of the resulting current in the loop.
A rectangular, 13-turn planar wire loop has a resistance of 0.13 Q and an area of 2.26 m². A magnetic field perpendicular to the plane's loop increases steadily from 54 mT to 203 mT in 1.75 s. Calculate the magnitude of the resulting current in the loop.
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![**Problem Statement:**
A rectangular, 13-turn planar wire loop has a resistance of 0.13 Ω and an area of 2.26 m². A magnetic field perpendicular to the plane's loop increases steadily from 54 mT to 203 mT in 1.75 s. Calculate the magnitude of the resulting current in the loop.
**Instructions:**
To solve this problem, we can use Faraday's Law of Induction, which relates the electromotive force (EMF) induced in the loop to the change in magnetic flux. The formula for EMF (ℰ) induced in a loop is:
\[ \text{ℰ} = -N \frac{\Delta \Phi}{\Delta t} \]
where:
- \( N \) is the number of turns in the loop (13 turns),
- \( \Delta \Phi \) is the change in magnetic flux,
- \( \Delta t \) is the time over which the change occurs.
The change in magnetic flux (ΔΦ) through the loop can be expressed as:
\[ \Delta \Phi = A \, \Delta B \]
where:
- \( A \) is the area of the loop (2.26 m²),
- \( \Delta B \) is the change in the magnetic field, calculated as:
\[ \Delta B = B_{\text{final}} - B_{\text{initial}} \]
The current (I) induced in the loop can be found using Ohm's law:
\[ I = \frac{\text{ℰ}}{R} \]
where \( R \) is the resistance of the loop (0.13 Ω).
Substitute the values into these formulas to find the current in the loop.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F047a7e6a-f025-4b5b-ab83-4ffe14f69253%2F042bfa33-296f-49e0-8e40-7f8d64e43633%2F3ucfjem_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A rectangular, 13-turn planar wire loop has a resistance of 0.13 Ω and an area of 2.26 m². A magnetic field perpendicular to the plane's loop increases steadily from 54 mT to 203 mT in 1.75 s. Calculate the magnitude of the resulting current in the loop.
**Instructions:**
To solve this problem, we can use Faraday's Law of Induction, which relates the electromotive force (EMF) induced in the loop to the change in magnetic flux. The formula for EMF (ℰ) induced in a loop is:
\[ \text{ℰ} = -N \frac{\Delta \Phi}{\Delta t} \]
where:
- \( N \) is the number of turns in the loop (13 turns),
- \( \Delta \Phi \) is the change in magnetic flux,
- \( \Delta t \) is the time over which the change occurs.
The change in magnetic flux (ΔΦ) through the loop can be expressed as:
\[ \Delta \Phi = A \, \Delta B \]
where:
- \( A \) is the area of the loop (2.26 m²),
- \( \Delta B \) is the change in the magnetic field, calculated as:
\[ \Delta B = B_{\text{final}} - B_{\text{initial}} \]
The current (I) induced in the loop can be found using Ohm's law:
\[ I = \frac{\text{ℰ}}{R} \]
where \( R \) is the resistance of the loop (0.13 Ω).
Substitute the values into these formulas to find the current in the loop.
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