A single loop of copper wire, lying flat in a plane, has an area of 7.20 cm? and a resistance of 2.10 Q. A uniform magnetic field points perpendicular to the plane of the loop. The field initially has a magnitude of 0.500 T, and the magnitude increases linearly to 2.00 T in a time of 1.06 s. What is the induced current (in mA) in the loop of wire over this time? mA

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**Induced Current Calculation in a Copper Loop**

**Problem Statement:**

A single loop of copper wire, lying flat in a plane, has the following characteristics:
- **Area:** 7.20 cm²
- **Resistance:** 2.10 Ω

A uniform magnetic field is oriented perpendicular to the plane of the loop. The magnetic field's initial magnitude is 0.500 T and increases linearly to 2.00 T within a time span of 1.06 s. 

**Question:** What is the induced current in milliamperes (mA) in the loop of wire over this time?

**Calculation Detail:**

To calculate the induced current (I) in the loop, we can use Faraday's Law of Electromagnetic Induction and Ohm's Law.

**1. Faraday's Law:**  
\( \mathcal{E} = -\frac{d\Phi_B}{dt} \)
   
Here, \( \mathcal{E} \) is the induced EMF (Electromotive Force), and \( \Phi_B \) is the magnetic flux, given by \( \Phi_B = B \cdot A \cdot \cos(\theta) \). Since the magnetic field is perpendicular to the loop, \(\cos(\theta) = \cos(0) = 1\), so \( \Phi_B = B \cdot A \).

**Change in Magnetic Flux \( (\Delta \Phi_B) \):**  
\( \Delta \Phi_B = A \cdot \Delta B = A \cdot (B_{\text{final}} - B_{\text{initial}}) \)

Here,  
\[ A = 7.20 \, \text{cm}^2 = 7.20 \times 10^{-4} \, \text{m}^2 \]  
\[ B_{\text{final}} = 2.00 \, \text{T} \]  
\[ B_{\text{initial}} = 0.500 \, \text{T} \]  

Therefore,  
\[ \Delta B = B_{\text{final}} - B_{\text{initial}} = 2.00 \, \text{T} - 0.500 \, \text{T} = 1.50 \, \text{T} \]

**Magnetic Flux Change:**  
\[ \Delta \
Transcribed Image Text:**Induced Current Calculation in a Copper Loop** **Problem Statement:** A single loop of copper wire, lying flat in a plane, has the following characteristics: - **Area:** 7.20 cm² - **Resistance:** 2.10 Ω A uniform magnetic field is oriented perpendicular to the plane of the loop. The magnetic field's initial magnitude is 0.500 T and increases linearly to 2.00 T within a time span of 1.06 s. **Question:** What is the induced current in milliamperes (mA) in the loop of wire over this time? **Calculation Detail:** To calculate the induced current (I) in the loop, we can use Faraday's Law of Electromagnetic Induction and Ohm's Law. **1. Faraday's Law:** \( \mathcal{E} = -\frac{d\Phi_B}{dt} \) Here, \( \mathcal{E} \) is the induced EMF (Electromotive Force), and \( \Phi_B \) is the magnetic flux, given by \( \Phi_B = B \cdot A \cdot \cos(\theta) \). Since the magnetic field is perpendicular to the loop, \(\cos(\theta) = \cos(0) = 1\), so \( \Phi_B = B \cdot A \). **Change in Magnetic Flux \( (\Delta \Phi_B) \):** \( \Delta \Phi_B = A \cdot \Delta B = A \cdot (B_{\text{final}} - B_{\text{initial}}) \) Here, \[ A = 7.20 \, \text{cm}^2 = 7.20 \times 10^{-4} \, \text{m}^2 \] \[ B_{\text{final}} = 2.00 \, \text{T} \] \[ B_{\text{initial}} = 0.500 \, \text{T} \] Therefore, \[ \Delta B = B_{\text{final}} - B_{\text{initial}} = 2.00 \, \text{T} - 0.500 \, \text{T} = 1.50 \, \text{T} \] **Magnetic Flux Change:** \[ \Delta \
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