### Induced Current in a Conducting Loop#### Problem Setup- **Coil Specifications:** - Diameter: 3.0 cm - Number of Turns: 18 - Location: \( z = 0 \) in the \( xy \)-plane - Current: 2.5 A- **Conducting Loop Specifications:** - Diameter: 2.0 mm - Resistance: \( 2.0 \times 10^{-4} \, \Omega \) - Initial Position: \( xy \)-plane at the center of the coil - Initial Time: \( t = 0 \, \text{s} \)- **Motion:** - The loop begins to move along the \( z \)-axis at a constant speed of 75 m/s.#### ObjectiveCalculate the induced current in the conducting loop at \( t = 200 \, \mu\text{s} \).#### Instructions- **Assumption:** The diameter of the conducting loop is much smaller than that of the coil. Assume the magnetic field through the loop is the on-axis field of the coil.- **Solution Approach:** Express the induced current \( I \) with appropriate units.#### CalculationThe students are expected to calculate the induced current using Faraday's Law of Induction and the properties provided. The small loop's motion and the coil's field must be considered in their calculations. Use the text box provided to input the current \( I \) in the specified units.

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A 3.0-cm-diameter, 18-turn coil of wire, located at z = 0 in the xy-plane, carries a current of 2.5 A. A 2.0-mm-diameter conducting loop with 2.0 x 10-4 resistance is also in the xy-plane at the center of the coil. At t = 0 s, the loop begins to move along the z-axis with a constant speed of 75 m/s. Part A What is the induced current in the conducting loop at t = 200 μs? The diameter of the conducting loop is much smaller than that of the coil, so you can assume that the magnetic field through the loop is everywhere the on-axis field of the coil. Express your answer with the appropriate units. I = μÀ Value Units ?

A 3.0-cm-diameter, 18-turn coil of wire, located at z = 0 in the xy-plane, carries a current of 2.5 A. A 2.0-mm-diameter conducting loop with 2.0 x 10-4 resistance is also in the xy-plane at the center of the coil. At t = 0 s, the loop begins to move along the z-axis with a constant speed of 75 m/s. Part A What is the induced current in the conducting loop at t = 200 μs? The diameter of the conducting loop is much smaller than that of the coil, so you can assume that the magnetic field through the loop is everywhere the on-axis field of the coil. Express your answer with the appropriate units. I = μÀ Value Units ?

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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Concept explainers

Voltage Across Inductor

An actor is a passive electrical component that consists of a coil bent in the form of wire which uses electromagnetism to produce electric current through the coil. When the electric current flows through a conductor that is the coil, a magnetic flux is developed around the conductor. This flow of current through the coil creates a magnetic field based on Fleming's Right-hand thumb rule. If there is any decrease in the current passing through the inductor, then the magnetic field will also decrease and energy is released through the generation of electric current. There is also a secondary voltage inducing in the same coil due to the magnetic flux, since it opposes any changes in the electric current flowing through the circuit. An inductor is also called choke, coil, or solenoid. A choke is designed to block certain frequencies when the DC current passes. A winding coil is coated with insulation to give extra insulation and protect the circuit. They are usually tightly wrapped around a central core which is cylindrical in nature so that the magnetic flux can be induced. The solenoid is a three-dimension coil that is used to exhibit electromagnetism when the magnetic field is developed due to the current flowing through the coil. The sign convention of the inductor is the same as the power dissipating device. When the current flows into the positive side of the voltage across the inductor, the value is positive and the inductor dissipates power whereas when the inductor releases the power back to the circuit, the current has a negative sign convention. 

Question

### Induced Current in a Conducting Loop

#### Problem Setup

- **Coil Specifications:**
- Diameter: 3.0 cm
- Number of Turns: 18
- Location: \( z = 0 \) in the \( xy \)-plane
- Current: 2.5 A

- **Conducting Loop Specifications:**
- Diameter: 2.0 mm
- Resistance: \( 2.0 \times 10^{-4} \, \Omega \)
- Initial Position: \( xy \)-plane at the center of the coil
- Initial Time: \( t = 0 \, \text{s} \)

- **Motion:**
- The loop begins to move along the \( z \)-axis at a constant speed of 75 m/s.

#### Objective

Calculate the induced current in the conducting loop at \( t = 200 \, \mu\text{s} \).

#### Instructions

- **Assumption:**
The diameter of the conducting loop is much smaller than that of the coil. Assume the magnetic field through the loop is the on-axis field of the coil.

- **Solution Approach:**
Express the induced current \( I \) with appropriate units.

#### Calculation

The students are expected to calculate the induced current using Faraday's Law of Induction and the properties provided. The small loop's motion and the coil's field must be considered in their calculations. Use the text box provided to input the current \( I \) in the specified units.

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