Triple Choice A region of space has a magnetic field that...

Triple Choice A region of space has a magnetic field that points out of the page. The field is uniform in the $y$ direction, but increases in strength in the positive $x$ direction, as indicated in Figure 23. 10. Four wire loops move through the region in different directions. For each of the loops, state whether its induced current is clockwise, counterclockwise, or zero.

Key Concepts

Motional EMF

Motional EMF arises when a conductor moves through a magnetic field, causing a separation of charge due to the Lorentz force acting on the charges. This phenomenon is a direct application of electromagnetic induction and results in an induced EMF even in regions of spatially varying magnetic fields.

Lenz's Law

Lenz's Law provides the direction of the induced current by ensuring that it always opposes the change in magnetic flux that produced it. This opposition is necessary to conserve energy and is essential for determining whether the induced current flows clockwise or counterclockwise.

Faraday's Law of Induction

Faraday's Law states that any change in the magnetic flux through a loop or circuit induces an electromotive force (EMF) in that loop. This law quantitatively relates the rate of flux change to the magnitude of the induced EMF.

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing perpendicularly through a surface, and changes in this flux (due to variations in field strength, loop area, or orientation) are what drive the induction process in electromagnetic systems.

Transcript

00:01 Okay, a region of space has a magnetic field that points out of the page, and the field is uniform in the y direction.

00:13 As you increase an x, the field increases.

00:20 Briefly draw what they have here.

00:23 As you increase x, the field strength increases.

00:30 And we have four loops one two three and four one two three and moving as i've drawn on the arrows here so we want to think about what direction is the induced current in the loop okay so we're using let the idea of lenz's law law here, which is the induced current will always flow in a direction that opposes the change that caused it.

01:15 Okay, the induced current will always move opposite or always move in a direction that opposes the change that caused it, so the change in flux.

01:27 So if we think, one, two, three, four, okay, easiest ones are two and four.

01:38 So if you think, look at two here, as it moves through the field, what happens to the flux through that ring? well, the flux is constant, so the flux does not change, so there's no induced current.

01:59 0, so 0.

02:02 Okay, same idea with number 4.

02:04 As it moves upward, the amount of flux passing through the loop does not change.

02:10 It's always constant.

02:11 It's the same amount of flux.

02:13 So there's no induced current.

02:17 Okay, and then if we're looking at number 1, as it moves to the right, the flux through it is increasing.

02:28 Okay, the flux through it is increasing in the z direction.

02:35 So flux is increasing...