
Concept explainers
![**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.](https://content.bartleby.com/qna-images/question/8edd889e-338a-4275-872c-5b2b400b4e22/e219fe1d-fb45-432c-8160-8b34f5d4d31a/od7juv_thumbnail.png)

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
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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