### Loop Moving into a Constant Magnetic FieldConsider a square loop with a side length of 1 m moving at a rate of 0.1 m/s in the +x direction into a magnetic field 6 m long with constant strength and direction of B = 1 T \( \hat{z} \) (into the page).**a. Magnetic Flux vs. Time Diagram**Sketch a diagram of the magnetic flux vs. time with \( t = 0 \) when the right edge of the square loop just starts to enter the magnetic field.- **Description**: - The magnetic flux (Φ) through the loop will change as the loop moves into the magnetic field. - When \( t = 0 \), the right edge of the loop just starts to enter the magnetic field. - As the loop continues to move into the field, the area inside the loop that is exposed to the magnetic field increases, causing the magnetic flux to increase. - When the entire loop is within the magnetic field, the magnetic flux reaches a maximum value. - Once the loop starts to exit the magnetic field, the magnetic flux begins to decrease. - The graph should show a linear increase in flux as the loop enters the field, a constant maximum flux when the loop is fully in the field, and a linear decrease as the loop exits the field.- **Graph Details**: - **X-axis**: Time (t) in seconds. - **Y-axis**: Magnetic Flux (Φ) in Weber (Wb).**b. Induced Electromotive Force (emf) Diagram**Sketch a diagram of the induced electromotive force (emf).- **Description**: - The induced emf in the loop is related to the rate of change of magnetic flux through Faraday's Law of Induction: \( \mathcal{E} = -\frac{dΦ}{dt} \). - When the loop first enters the magnetic field, the rate of change of flux is positive, inducing a positive emf. - When the loop is fully within the magnetic field, the flux is constant, and thus the induced emf is zero. - As the loop exits the magnetic field, the rate of change of flux is negative, inducing a negative emf. - The graph should show a positive peak when entering, zero when the entire loop is within the field, and a negative peak when exiting.- **

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1. Loop moving into a Constant Magnetic Field. Consider a square loop with side length 1m moving at a rate 0.1 m/s in the +x-direction into a magnetic field 6m long with constant strength and direction of B = 1 T 2 (into the page). a. Sketch a diagram of the magnetic flux vs. time with t=0 when the right edge of the square loop just starts to enter the magnetic field. b. Sketch a diagram of the induced electromotive force.

1. Loop moving into a Constant Magnetic Field. Consider a square loop with side length 1m moving at a rate 0.1 m/s in the +x-direction into a magnetic field 6m long with constant strength and direction of B = 1 T 2 (into the page). a. Sketch a diagram of the magnetic flux vs. time with t=0 when the right edge of the square loop just starts to enter the magnetic field. b. Sketch a diagram of the induced electromotive force.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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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Question

### Loop Moving into a Constant Magnetic Field

Consider a square loop with a side length of 1 m moving at a rate of 0.1 m/s in the +x direction into a magnetic field 6 m long with constant strength and direction of B = 1 T \( \hat{z} \) (into the page).

**a. Magnetic Flux vs. Time Diagram**

Sketch a diagram of the magnetic flux vs. time with \( t = 0 \) when the right edge of the square loop just starts to enter the magnetic field.

- **Description**:
- The magnetic flux (Φ) through the loop will change as the loop moves into the magnetic field.
- When \( t = 0 \), the right edge of the loop just starts to enter the magnetic field.
- As the loop continues to move into the field, the area inside the loop that is exposed to the magnetic field increases, causing the magnetic flux to increase.
- When the entire loop is within the magnetic field, the magnetic flux reaches a maximum value.
- Once the loop starts to exit the magnetic field, the magnetic flux begins to decrease.
- The graph should show a linear increase in flux as the loop enters the field, a constant maximum flux when the loop is fully in the field, and a linear decrease as the loop exits the field.

- **Graph Details**:
- **X-axis**: Time (t) in seconds.
- **Y-axis**: Magnetic Flux (Φ) in Weber (Wb).

**b. Induced Electromotive Force (emf) Diagram**

Sketch a diagram of the induced electromotive force (emf).

- **Description**:
- The induced emf in the loop is related to the rate of change of magnetic flux through Faraday's Law of Induction: \( \mathcal{E} = -\frac{dΦ}{dt} \).
- When the loop first enters the magnetic field, the rate of change of flux is positive, inducing a positive emf.
- When the loop is fully within the magnetic field, the flux is constant, and thus the induced emf is zero.
- As the loop exits the magnetic field, the rate of change of flux is negative, inducing a negative emf.
- The graph should show a positive peak when entering, zero when the entire loop is within the field, and a negative peak when exiting.

- **

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