The component of the external magnetic field along the central axis of a 33 turn circular coil of radius 27.0 cm decreases from 1.90 T to 0.400 T in 2.90 s. If the resistance of the coil is R = 6.00 52, what is the magnitude of the induced current in the coil? magnitude: What is the direction of the current if the axial component of the field points away from the viewer? O counter-clockwise
The component of the external magnetic field along the central axis of a 33 turn circular coil of radius 27.0 cm decreases from 1.90 T to 0.400 T in 2.90 s. If the resistance of the coil is R = 6.00 52, what is the magnitude of the induced current in the coil? magnitude: What is the direction of the current if the axial component of the field points away from the viewer? O counter-clockwise
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![## Induced Current in a Circular Coil
**Problem Statement:**
The component of the external magnetic field along the central axis of a 33 turn circular coil of radius 27.0 cm decreases from 1.90 T to 0.400 T in 2.90 s. If the resistance of the coil is \( R = 6.00 \, \Omega \), what is the magnitude of the induced current in the coil?
- **Magnitude:** \( \boxed{} \, \text{A} \)
### Direction of the Induced Current:
- What is the direction of the current if the axial component of the field points away from the viewer?
- [ ] Counter-clockwise
- [ ] Clockwise
### Explanation:
To find the induced current in the coil, we use Faraday's Law of Induction which states that the induced electromotive force (emf) in the coil is given by:
\[ \mathcal{E} = -N \frac{d\Phi_B}{dt} \]
Where:
- \( N \) is the number of turns
- \( \Phi_B \) is the magnetic flux
- \( \frac{d\Phi_B}{dt} \) is the rate of change of magnetic flux
The magnetic flux \( \Phi_B \) through one turn of the coil is given by:
\[ \Phi_B = B \cdot A \]
Where:
- \( B \) is the magnetic field
- \( A \) is the area of the coil (\( A = \pi r^2 \))
Given data:
- \( N = 33 \)
- \( r = 27.0 \, \text{cm} = 0.270 \, \text{m} \)
- \( B \) changes from \( 1.90 \, \text{T} \) to \( 0.400 \, \text{T} \) in \( 2.90 \, \text{s} \)
- \( R = 6.00 \, \Omega \)
The change in magnetic flux \( \Delta \Phi_B \) is:
\[ \Delta \Phi_B = \Phi_B (\text{final}) - \Phi_B (\text{initial}) \]
\[ \Delta \Phi_B = (0.400 \, \text{T} \cdot \pi \cdot (0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78db42f9-6d62-48c9-a117-b436e469106b%2Fce7c01b8-0679-4cdc-96ed-fc8b5811475e%2Fqnz9rgq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Induced Current in a Circular Coil
**Problem Statement:**
The component of the external magnetic field along the central axis of a 33 turn circular coil of radius 27.0 cm decreases from 1.90 T to 0.400 T in 2.90 s. If the resistance of the coil is \( R = 6.00 \, \Omega \), what is the magnitude of the induced current in the coil?
- **Magnitude:** \( \boxed{} \, \text{A} \)
### Direction of the Induced Current:
- What is the direction of the current if the axial component of the field points away from the viewer?
- [ ] Counter-clockwise
- [ ] Clockwise
### Explanation:
To find the induced current in the coil, we use Faraday's Law of Induction which states that the induced electromotive force (emf) in the coil is given by:
\[ \mathcal{E} = -N \frac{d\Phi_B}{dt} \]
Where:
- \( N \) is the number of turns
- \( \Phi_B \) is the magnetic flux
- \( \frac{d\Phi_B}{dt} \) is the rate of change of magnetic flux
The magnetic flux \( \Phi_B \) through one turn of the coil is given by:
\[ \Phi_B = B \cdot A \]
Where:
- \( B \) is the magnetic field
- \( A \) is the area of the coil (\( A = \pi r^2 \))
Given data:
- \( N = 33 \)
- \( r = 27.0 \, \text{cm} = 0.270 \, \text{m} \)
- \( B \) changes from \( 1.90 \, \text{T} \) to \( 0.400 \, \text{T} \) in \( 2.90 \, \text{s} \)
- \( R = 6.00 \, \Omega \)
The change in magnetic flux \( \Delta \Phi_B \) is:
\[ \Delta \Phi_B = \Phi_B (\text{final}) - \Phi_B (\text{initial}) \]
\[ \Delta \Phi_B = (0.400 \, \text{T} \cdot \pi \cdot (0
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