Chapter 21, Problem 5Q

(a)

To determine

To Explain: Whether the current will induce or not.

Answer to Problem 5Q

Yes, current will be induced in the battery.

Explanation of Solution

Introduction:Faraday’s law of induction is the fundamental law of electromagnetism. According to this law,

  $EMF=-N\frac{\Delta {\varphi }_B}{\Delta t}$

In the equation, $EMF=-N\frac{\Delta {\varphi }_B}{\Delta t}$ , minus sign represents direction the induced EMF acts. As per given experiment, when the battery is connected, current will be flow. The changing current generates a changing magnetic field. This magnetic field induces a current in another loop.

(b)

To determine

To Explain: Starting time of the current.

Answer to Problem 5Q

The current will start flowing immediately.

Explanation of Solution

Introduction:Faraday’s law of induction is the fundamental law of electromagnetism. According to this law,

  $EMF=-N\frac{\Delta {\varphi }_B}{\Delta t}$

In the equation, $EMF=-N\frac{\Delta {\varphi }_B}{\Delta t}$ , minus sign represents direction the induced EMF acts. As per given experiment, when the battery is connected, current will flow. The changing current generates a changing magnetic field. This magnetic field induces a current in another loop. The induced current in second loop starts flowing as soon as current in the front loop starts to increase creating a magnetic field.

(c)

To determine

To Explain: the time when the current will stop flowing.

Answer to Problem 5Q

The current stops at steady state.

Explanation of Solution

Introduction:Faraday’s law of induction is the fundamental law of electromagnetism. According to this law,

  $EMF=-N\frac{\Delta {\varphi }_B}{\Delta t}$

In the equation, $EMF=-N\frac{\Delta {\varphi }_B}{\Delta t}$ , minus sign represents direction the induced EMF acts. As per given experiment, when the battery is connected, current will flow. The changing current generates a changing magnetic field. This magnetic field induces a current in another loop. The induced current in second loop starts flowing as soon as current in the front loop starts to increase and creates a magnetic field. But when the current reaches a steady state, this induced current will stop flowing.

Reason for this is zero change in the magnetic field. So, zero change will be occurred in the magnetic flux.

(d)

To determine

To Explain: Direction of flowing current.

Answer to Problem 5Q

The direction of current will be counter clockwise.

Explanation of Solution

Introduction:Faraday’s law of induction is the fundamental law of electromagnetism. According to this law,

  $EMF=-N\frac{\Delta {\varphi }_B}{\Delta t}$

In the equation, $EMF=-N\frac{\Delta {\varphi }_B}{\Delta t}$ , minus sign represents direction the induced EMF acts. As per given experiment, when the battery is connected, current will be flow.

By the Lenz’s law obtain the direction of the current which forms a magnetic field that reduces the magnetic flux. In the given experiment, increasing clockwise current in the front loop is causing an increase in the strength of the magnetic field. Lenz’s law states that the second loop will attempt to oppose this change in flux. This will be done if the induced current flows counterclockwise. So, a counter clockwise (direction) current will be created because the magnetic flux is varying.

(e)

To determine

To Explain: Whether there is force between the two loops or not.

Answer to Problem 5Q

Yes, there is force between the two loops.

Explanation of Solution

Introduction:Faraday’s law of induction is the fundamental law of electromagnetism. According to this law,

  $EMF=-N\frac{\Delta {\varphi }_B}{\Delta t}$

In the equation, $EMF=-N\frac{\Delta {\varphi }_B}{\Delta t}$ , minus sign represents direction the induced EMF acts. As per given experiment, when the battery is connected, current will be flow.

In a given experiment, both loops carry current and create magnetic field while the current in the front loop is increasing form the battery. So, these two magnetic fields will be interactingand also, place a force on each loop.

(f)

To determine

To Explain: The direction in which a force between the two loops.

Answer to Problem 5Q

The direction of two loops will be opposite to each other.

Explanation of Solution

Introduction:Faraday’s law of induction is the fundamental law of electromagnetism. According to this law,

  $EMF=-N\frac{\Delta {\varphi }_B}{\Delta t}$

In the equation, $EMF=-N\frac{\Delta {\varphi }_B}{\Delta t}$ , minus sign represents direction the induced EMF acts. As per given experiment, when the battery is connected, current will be flow.

In a given experiment, both loops carry current and create magnetic field while the current in the front loop is increasing form the battery. So, these two magnetic fields will be interacting and also, place a force on each loop.

The loop of front side will create a magnetic field pointed in the direction of the second loop. Also, this varying magnetic field induces current in second loop to oppose/ repelan increasing magnetic field. This induced current generates a magnetic field pointing in the direction of the front loop. So, both two magnetic fields will work as two north poles or ends pointing toward at each otherand repel.