A circular conducting loop of radius 26.6 cm and resistance 4.2 is held at rest in the x-y plane. A uniform but time varying magnetic field exists which can point either out of the page (+z) or into the page (-z). The z-component of the magnetic field changes according to the graph shown. • From t = 0 s to t = 4.6 s, the magnetic field is given by: B(t) = Ct³ where C is a constant with value C = 55 mT/s³. • From t = 4.6 s to t = 7 s, the magnetic field has a constant value of Bo. • From t = 7 s to t = 12.5 s, the magnetic field linearly decreases from Bo to -Bo/2.
A circular conducting loop of radius 26.6 cm and resistance 4.2 is held at rest in the x-y plane. A uniform but time varying magnetic field exists which can point either out of the page (+z) or into the page (-z). The z-component of the magnetic field changes according to the graph shown. • From t = 0 s to t = 4.6 s, the magnetic field is given by: B(t) = Ct³ where C is a constant with value C = 55 mT/s³. • From t = 4.6 s to t = 7 s, the magnetic field has a constant value of Bo. • From t = 7 s to t = 12.5 s, the magnetic field linearly decreases from Bo to -Bo/2.
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Transcribed Image Text:A circular conducting loop of radius 26.6 cm and resistance 4.2 Ω is held at rest in the x-y plane. A uniform but time-varying magnetic field exists which can point either out of the page (+z) or into the page (-z). The z-component of the magnetic field changes according to the graph shown.
- From \( t = 0 \, \text{s} \) to \( t = 4.6 \, \text{s} \), the magnetic field is given by: \( B(t) = Ct^3 \) where \( C \) is a constant with value \( C = 55 \, \text{mT/s}^3 \).
- From \( t = 4.6 \, \text{s} \) to \( t = 7 \, \text{s} \), the magnetic field has a constant value of \( B_0 \).
- From \( t = 7 \, \text{s} \) to \( t = 12.5 \, \text{s} \), the magnetic field linearly decreases from \( B_0 \) to \( -B_0/2 \).
### Diagram Explanation:
- **Left Diagram**: Shows the circular loop in the x-y plane and the region where the magnetic field \( B \) is present.
- **Right Graph**: Displays the time-dependent behavior of the magnetic field's z-component \( B_z \) against time \( t \):
- **Curve (0 to \( t_1 \))**: Represents the increase of the magnetic field following a cubic relation.
- **Horizontal Line (\( t_1 \) to \( t_2 \))**: Represents the constant magnetic field value \( B_0 \).
- **Slope (\( t_2 \) to \( t_3 \))**: Represents the linear decrease in magnetic field from \( B_0 \) to \( -B_0/2 \).
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### Questions:
1) **What is the magnitude of the magnetic flux through the loop at \( t = 3 \, \text{s} \)? Enter your answer in units of \( T \cdot \text{m}^2 \).**
Answer Box:
```
T · m²
```
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