A coil of wire consists of 20 turns each of which has an area of 0.0015 m². A magnetic field is perpendicular to the surface. Initially, the magnitude of the magnetic field is 0.050 T and 0.10s later, it has increased to 0.060 T. Find the average e m f induced in the coil during this time.
A coil of wire consists of 20 turns each of which has an area of 0.0015 m². A magnetic field is perpendicular to the surface. Initially, the magnitude of the magnetic field is 0.050 T and 0.10s later, it has increased to 0.060 T. Find the average e m f induced in the coil during this time.
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Problem Statement
A coil of wire consists of 20 turns, each of which has an area of \(0.0015 \, m^2\). A magnetic field is perpendicular to the surface. Initially, the magnitude of the magnetic field is \(0.050 \, T\) and 0.1s later, it has increased to \(0.060 \, T\). Find the average e.m.f induced in the coil during this time.
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To solve this problem, we need to utilize Faraday's Law of Induction which states that the induced electromotive force (e.m.f) in any closed circuit is equal to the negative rate of change of the magnetic flux through the circuit:
\[ \text{emf} = -N \frac{\Delta \Phi}{\Delta t} \]
Where:
- \( N \) is the number of turns in the coil
- \( \Delta \Phi \) is the change in magnetic flux
- \( \Delta t \) is the change in time
### Step-by-Step Solution
#### Step 1: Calculate Magnetic Flux
The magnetic flux \( \Phi \) is given by:
\[ \Phi = B \times A \]
Where:
- \( B \) is the magnetic field
- \( A \) is the area of the coil
Initial magnetic flux \( \Phi_i \):
\[ \Phi_i = 0.050 \, T \times 0.0015 \, m^2 = 0.000075 \, Wb \]
(Wb is the Weber unit of magnetic flux)
Final magnetic flux \( \Phi_f \):
\[ \Phi_f = 0.060 \, T \times 0.0015 \, m^2 = 0.00009 \, Wb \]
#### Step 2: Find Change in Magnetic Flux
\[ \Delta \Phi = \Phi_f - \Phi_i = 0.00009 \, Wb - 0.000075 \, Wb = 0.000015 \, Wb \]
#### Step 3: Calculate the Change in Time
\[ \Delta t = 0.1 \, s \]
#### Step 4: Substitute Values in Faraday’s Law
\[ \text{emf} = -N \frac{\Delta \Phi}{\Delta t} \]
\[ \text{emf} = -20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4eb8153a-3a83-4b3e-b817-a98859d3685f%2Fc98444bb-d78d-4f8d-963d-a1515dba08ba%2Fb8hv0wk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
A coil of wire consists of 20 turns, each of which has an area of \(0.0015 \, m^2\). A magnetic field is perpendicular to the surface. Initially, the magnitude of the magnetic field is \(0.050 \, T\) and 0.1s later, it has increased to \(0.060 \, T\). Find the average e.m.f induced in the coil during this time.
---
To solve this problem, we need to utilize Faraday's Law of Induction which states that the induced electromotive force (e.m.f) in any closed circuit is equal to the negative rate of change of the magnetic flux through the circuit:
\[ \text{emf} = -N \frac{\Delta \Phi}{\Delta t} \]
Where:
- \( N \) is the number of turns in the coil
- \( \Delta \Phi \) is the change in magnetic flux
- \( \Delta t \) is the change in time
### Step-by-Step Solution
#### Step 1: Calculate Magnetic Flux
The magnetic flux \( \Phi \) is given by:
\[ \Phi = B \times A \]
Where:
- \( B \) is the magnetic field
- \( A \) is the area of the coil
Initial magnetic flux \( \Phi_i \):
\[ \Phi_i = 0.050 \, T \times 0.0015 \, m^2 = 0.000075 \, Wb \]
(Wb is the Weber unit of magnetic flux)
Final magnetic flux \( \Phi_f \):
\[ \Phi_f = 0.060 \, T \times 0.0015 \, m^2 = 0.00009 \, Wb \]
#### Step 2: Find Change in Magnetic Flux
\[ \Delta \Phi = \Phi_f - \Phi_i = 0.00009 \, Wb - 0.000075 \, Wb = 0.000015 \, Wb \]
#### Step 3: Calculate the Change in Time
\[ \Delta t = 0.1 \, s \]
#### Step 4: Substitute Values in Faraday’s Law
\[ \text{emf} = -N \frac{\Delta \Phi}{\Delta t} \]
\[ \text{emf} = -20
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