College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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**Title: Induction in a Circular Coil Due to a Moving Current-Carrying Wire**

**Introduction:**
The image depicts a scenario involving electromagnetic induction. A long straight wire carrying a constant current of 2.13 A moves with a constant speed to the right. A 120-turn circular coil, having a diameter of 1.50 cm and a resistance of 3.25 μΩ, is placed in the same plane as the straight wire. Initially, the wire is positioned to the left of the coil, at a distance of d = 14.0 cm from the center. After 5.00 seconds, the wire relocates to the right of the coil, maintaining the same distance from its center.

**Diagrams Description:**
- Two diagrams illustrate two situations: the initial and final positions of the straight wire relative to the coil.
- In both diagrams, the wire is shown as a vertical line carrying a current (I) downward; its velocity (v) is directed towards the right.
- The coil is represented as a circle with a center-to-wire distance marked as "d."

**Questions and Options:**

(a) **Initial Situation (Wire Moving Toward the Coil):**  
What is the direction of the induced current in the coil when the wire moves towards it?
- Clockwise
- Counterclockwise
- No current

(b) **Final Situation (Wire Moving Away from the Coil):**  
What is the direction of the induced current in the coil when the wire moves away?
- Clockwise
- Counterclockwise
- No current

(c) **Average Induced Current Calculation:**  
What is the magnitude of the average induced current in the coil over the 5.00-second interval?  
\[ \_\_\_ \text{mA} \]

**Conclusion:**
This exercise demonstrates the principles of electromagnetic induction, specifically analyzing how the motion of a current-carrying conductor relative to a coil affects induced currents within the coil. Understanding these effects is fundamental in electromagnetism and its applications in electrical engineering and physics.
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Transcribed Image Text:**Title: Induction in a Circular Coil Due to a Moving Current-Carrying Wire** **Introduction:** The image depicts a scenario involving electromagnetic induction. A long straight wire carrying a constant current of 2.13 A moves with a constant speed to the right. A 120-turn circular coil, having a diameter of 1.50 cm and a resistance of 3.25 μΩ, is placed in the same plane as the straight wire. Initially, the wire is positioned to the left of the coil, at a distance of d = 14.0 cm from the center. After 5.00 seconds, the wire relocates to the right of the coil, maintaining the same distance from its center. **Diagrams Description:** - Two diagrams illustrate two situations: the initial and final positions of the straight wire relative to the coil. - In both diagrams, the wire is shown as a vertical line carrying a current (I) downward; its velocity (v) is directed towards the right. - The coil is represented as a circle with a center-to-wire distance marked as "d." **Questions and Options:** (a) **Initial Situation (Wire Moving Toward the Coil):** What is the direction of the induced current in the coil when the wire moves towards it? - Clockwise - Counterclockwise - No current (b) **Final Situation (Wire Moving Away from the Coil):** What is the direction of the induced current in the coil when the wire moves away? - Clockwise - Counterclockwise - No current (c) **Average Induced Current Calculation:** What is the magnitude of the average induced current in the coil over the 5.00-second interval? \[ \_\_\_ \text{mA} \] **Conclusion:** This exercise demonstrates the principles of electromagnetic induction, specifically analyzing how the motion of a current-carrying conductor relative to a coil affects induced currents within the coil. Understanding these effects is fundamental in electromagnetism and its applications in electrical engineering and physics.
Expert Solution
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Step 1

Induced current:

The current induced in a conducting loop that is exposed to a changing magnetic field is known as induced current.

Explanation:

Current through the straight wire, I = 2.13 A

Number of turns, N = 120 turns

Diameter of the coil, D = 1.50 cm

Resistance of the coil, 

Distance of the wire from the center of the coil, d = 14 cm = 0.14 m

The magnetic field, B₁, when the wire is at a distance, d, from the center of the coil.

B1=μ0I2πd     =4π×10-7(2.13)2π(0.14)     =30.43×10-7 T

 

 

Step 2

Magnetic field B₂ when the wire is at a distance, 2d from the center of the coil

B2=μ0I2π(2d)     =4π×10-7(2.13)2π(0.14)2     =15.21×10-7 T

Change in the magnetic field, ΔB = B₂ - B₁ = 15.22×10-7 T

Induced current, 

E = -N (Δ∅)/Δt

Δ∅ = A ΔB

Area, A = πr²

diameter, D = 0.015 m

Radius, r = 0.0075 m

A = π×0.0075²

A = 0.000176625 m²

 

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