A long straight wire carrying a current of 2.13 A moves with a constant speed v to the right. A 120 turn circular coil of diameter 1.50 cm, and resistance of 3.25 pn, lies stationary in the same plane as the straight wire. At some initial time the wire is to the left of the coil at a distance d = 14.0 cm from its center. 5.00 s later, the wire has moved to the right of the coil and is at a distance d from the center of the coil. You may assume for simplicity that the magnetic field is uniform in the region of the coil. Initial situation Final situation (a) what is the direction the induced current in the coil as the wire moves toward the coil, in the initial situation? O clockwise O counterclockwise O no current (b) What is the direction of the induced current in the coil as the wire moves away from coil, in the final situation? O clockwise O counterclockwise O no current (c) What is the magnitude of the average induced current in the coil over the 5.00 s interval?

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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.
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
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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