Concept explainers
Review Question 21.1 Your friend thinks that relative motion of a coil and a magnet is absolutely necessary to induce current in a coil that is not connected to a battery Support your friend’s point of view with a physics argument. Then provide a counterargument and describe an experiment you could perform to disprove your friend's idea.

A physics argument that relative motion between a magnet and a coil is absolutely necessary to induce current in the coil which is not connected to a battery. Also, provide a counterargument and disprove the above statement with the help of an experiment.
Answer to Problem 1RQ
Solution:
“Whenever the magnetic field flux through an area which is enclosed by a closed conducting loop (coil) changes, a current is induced in the loop (coil)”. So, in order to change the flux, a relative motion between the coil and the magnet must be provided.
A counterstatement for the above statement is, ‘in order to induce current in the coil, the magnetic flux can be changed in a number of ways and not just by providing a relative motion between the magnet and coil.’ The flux can be changed by manipulating the magnitude of the magnetic field
Experiment- Take a magnet with a controllable magnetic field, and fix its position relative to the coil. Now increase the magnitude of the magnetic field. As the field changes, it produces a change in the magnetic flux, thus inducing an EMF and hence, a current is induced in the coil without relative motion between the magnet and the coil.
Explanation of Solution
Introduction:
Whenever the magnetic field flux through an area which is enclosed by a closed conducting loop (coil) changes, an EMF (Electromotive force) is produced in the loop.
The equation for Faraday’s Law of Electromagnetic Induction is:
Here,
Explanation:
According to Faraday’s Law, whenever there is a change in the magnetic flux of the coil, an EMF is induced in the coil. The induced EMF results in an induced current inside the coil. The most common way to produce this EMF is to move the magnet or magnetic field relative to the coil or vice versa. By doing so, the flux across the coil changes and current is induced.
But contradictory to the general belief, the magnetic flux can be changed by other ways also. One way to change the magnetic flux is to change the magnitude of the magnetic field at the site of the loop.
Consider a coil of area
Now, write the expression for magnetic flux.
And,
Here,
Substitute
Similarly, substitute
Now, the equation of induced EMF (
Here,
Substitute
Induced current
Here,
Substitute
Here, the negative sign denotes the direction of EMF.
Hence, an induced current has been achieved without the relative motion of the coil and magnet.
As discussed in the experiment, a change in the magnitude of magnetic field results in an induced current.
Another way is to change the area of the loop. The magnetic flux (
So, a change in area causes a change in magnetic flux, thereby inducing a current in the coil.
Also, a change in the direction of area vector and magnetic field vector can cause an induced current to develop in the coil.
Conclusion:
The statement that a relative motion between the coil and the magnet is absolutely necessary, has been subjected to a physics argument. A counterstatement has also been provided, which is proven with the help of an experiment that current in a coil can also be induced by changing the magnetic field, as given by Faraday’s law.
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Chapter 21 Solutions
College Physics: Explore And Apply, Volume 2 (2nd Edition)
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