The magnetic field in the picture is uniform and into the page.
Suppose that the loop is flexible, and that its radius is decreasing with time. Assume that the magnetic flux through the loop is positive when the magnetic field points into the page.
The magnetic flux through the loop is ing (increasing/decreasing)
The induced magnetic field will cause the flux through the loop to e(increase/decrease)
The induced magnetic field points the page (into/out of)
The induced current in the loop circulates (clockwise/counterclockwise)
The Correct Answer and Explanation is :
Based on the scenario where the radius of a flexible loop is decreasing in a uniform magnetic field directed into the page, we can apply Faraday’s Law of Induction to determine the changes in flux and the induced current.
- The magnetic flux through the loop is decreasing.
The magnetic flux (Φ) through the loop is given by the equation:
[
\Phi = B \cdot A
]
where ( B ) is the magnetic field strength and ( A ) is the area of the loop. As the radius of the loop decreases, the area of the loop decreases, and thus the magnetic flux through the loop decreases, because the magnetic field strength is constant, and the area is shrinking. - The induced magnetic field will cause the flux through the loop to increase.
According to Lenz’s Law, the induced current will generate a magnetic field that opposes the change in flux. Since the flux through the loop is decreasing, the induced current will produce a magnetic field that tries to increase the flux, i.e., it will attempt to make the flux through the loop more positive. - The induced magnetic field points out of the page.
To oppose the decrease in flux, the induced magnetic field must point out of the page. This is because the original magnetic field is into the page, and by Lenz’s Law, the induced field must oppose the reduction of flux caused by the shrinking area, thus it points in the opposite direction, out of the page. - The induced current in the loop circulates counterclockwise.
To create a magnetic field out of the page, the direction of the induced current must be counterclockwise. This is determined using the right-hand rule: when the fingers of the right hand curl in the direction of the current, the thumb points in the direction of the magnetic field. For the induced field to point out of the page, the current must circulate counterclockwise.
In conclusion, as the loop’s radius decreases, the flux decreases, and the induced current circulates counterclockwise, generating a magnetic field out of the page to oppose the change in flux.