### Inducing a Counterclockwise Current in a Loop**Problem Statement:**A long straight wire carries a current $ I_0 $ as shown below. There is initially no current in the loop. In which direction should the loop be moved in order to induce a counterclockwise current in it?**Diagram Explanation:**- A vertical line represents the long straight wire carrying current $ I_0 $.- To the left of the wire, there is a horizontal dashed line indicating the direction in which the loop should be moved.- An upward dotted arrow is shown next to the wire, labeled "up".**Approach:**To solve the problem, use the concept of electromagnetic induction (Faraday's Law) which states that a change in magnetic flux through a closed loop induces an electromotive force (EMF) around the loop. The direction of the induced current is given by Lenz's Law, which states that the induced current will flow in a direction such that it opposes the change in magnetic flux.1. **Magnetic Field around the Wire:** - The magnetic field ($ B $) around a long straight current-carrying wire forms concentric circles with the wire at the center. - By the right-hand rule, with the thumb pointing in the direction of the current ($ I_0 $), the fingers curl around the wire in the direction of the magnetic field. - For an upward current ($ I_0 $), the magnetic field around the wire circulates counterclockwise when viewing the wire from above.2. **Change in Magnetic Flux:** - The loop needs to be moved in such a way that the magnetic flux through it changes. - If the loop is moved to the left, towards the wire, the magnetic flux passing through the loop increases. - If the loop is moved to the right, away from the wire, the magnetic flux through the loop decreases.3. **Inducing Counterclockwise Current:** - To induce a counterclockwise current in the loop (using Lenz's Law), the loop needs to be moved in such a direction that it opposes the increase in magnetic flux. - Moving the loop to the right would decrease the magnetic flux through the loop because it moves away from the source of the magnetic field. This would induce a current in the loop that creates a magnetic field to oppose the decrease — in this case creating a magnetic field

The magnetic field produced by the straight wire gets stronger when we go towards the wire. B ∝ 1/r…

A long straight wire carries a current I, as shown below. There is initially no current in the loop. In which direction should the loop be moved in order to induce a counterclockwise current in it? Hig A I I I up I ---->>

A long straight wire carries a current I, as shown below. There is initially no current in the loop. In which direction should the loop be moved in order to induce a counterclockwise current in it? Hig A I I I up I ---->>

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

### Inducing a Counterclockwise Current in a Loop

**Problem Statement:**
A long straight wire carries a current $ I_0 $ as shown below. There is initially no current in the loop. In which direction should the loop be moved in order to induce a counterclockwise current in it?

**Diagram Explanation:**
- A vertical line represents the long straight wire carrying current $ I_0 $.
- To the left of the wire, there is a horizontal dashed line indicating the direction in which the loop should be moved.
- An upward dotted arrow is shown next to the wire, labeled "up".

**Approach:**
To solve the problem, use the concept of electromagnetic induction (Faraday's Law) which states that a change in magnetic flux through a closed loop induces an electromotive force (EMF) around the loop. The direction of the induced current is given by Lenz's Law, which states that the induced current will flow in a direction such that it opposes the change in magnetic flux.

1. **Magnetic Field around the Wire:**
- The magnetic field ($ B $) around a long straight current-carrying wire forms concentric circles with the wire at the center.
- By the right-hand rule, with the thumb pointing in the direction of the current ($ I_0 $), the fingers curl around the wire in the direction of the magnetic field.
- For an upward current ($ I_0 $), the magnetic field around the wire circulates counterclockwise when viewing the wire from above.

2. **Change in Magnetic Flux:**
- The loop needs to be moved in such a way that the magnetic flux through it changes.
- If the loop is moved to the left, towards the wire, the magnetic flux passing through the loop increases.
- If the loop is moved to the right, away from the wire, the magnetic flux through the loop decreases.

3. **Inducing Counterclockwise Current:**
- To induce a counterclockwise current in the loop (using Lenz's Law), the loop needs to be moved in such a direction that it opposes the increase in magnetic flux.
- Moving the loop to the right would decrease the magnetic flux through the loop because it moves away from the source of the magnetic field. This would induce a current in the loop that creates a magnetic field to oppose the decrease — in this case creating a magnetic field

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