In problems 1 through 7, select the best answer to make the...

In problems 1 through 7, select the best answer to make the statement true, and place the letter of the answer in the space provided. Maximum voltage is induced in a single loop when the sides of the loop are passing_____ a. perpendicular to the lines of force. b. parallel to the lines of force. c. not quite perpendicular to the lines of force. d. at a slow rate of speed. e. in front of the $\mathrm{N}$ pole face.

In problems 1 through 7, select the best answer to make the statement true, and place the letter of the answer in the space provided.
Maximum voltage is induced in a single loop when the sides of the loop are passing_____
a. perpendicular to the lines of force.
b. parallel to the lines of force.
c. not quite perpendicular to the lines of force.
d. at a slow rate of speed.
e. in front of the $\mathrm{N}$ pole face.

Key Concepts

Orientation of the Loop Relative to the Magnetic Field

The orientation of a loop relative to a magnetic field critically affects the amount of magnetic flux through the loop and thus the induced emf. When the plane of the loop is perpendicular to the magnetic field lines, the effective area through which the field penetrates is maximized, leading to a larger induced voltage when the field strength changes.

Magnetic Flux

Magnetic flux refers to the quantity of magnetic field passing through a given area. It is an important concept in understanding electromagnetic induction, as the induced emf in a loop is directly related to the time rate of change of this flux. The flux is maximized when the loop's area is oriented perpendicular to the direction of the magnetic field.

Electromagnetic Induction

Electromagnetic induction is the process by which a changing magnetic field produces an electric current in a conductor. It is a foundational concept in electromagnetism and is mathematically described by Faraday's law, which relates the induced electromotive force (emf) to the rate of change of magnetic flux through a closed circuit.

Transcript

00:01 In this problem, we're asked to consider a circular loop of wire moving in the xy plane with constant velocity in the negative x direction, and it enters a uniform magnetic field which covers the region in which x is less than zero.

00:17 The surface normal vector of the loop points in the direction of the magnetic field.

00:24 Knowing this, which statement is correct.

00:28 Statement a says, induced potential difference.

00:33 In the loop is at a maximum as the edge of the loop just enters the region with magnetic field.

01:31 Okay.

01:36 Okay.

01:36 So we're going to be observing the conductive loop moving in the x, y plane, as shown in the figure below.

01:45 So let me do a little thinking here.

01:49 I'm going to go get a black, and i'm going to have my y direction.

02:02 Here i've got a circular loop.

02:04 Here's my x direction.

02:08 And i've got all of these charges.

02:11 I'm not going to draw all my charges in.

02:15 And we've got this.

02:17 Okay, the magnetic field lines are represented.

02:25 These are magnetic fields lines.

02:41 And they're directed from the drawing towards us, and they're parallel to the normal vector of the loop of the wire.

02:49 And we're determining which position of the loop of the wire, of the loop of wire relative to the region of uniform magnetic field is a potential difference induced in the maximum loop.

03:05 The loop is divided into four quarters since we need to determine under which overlap.

03:13 Okay.

03:14 So let me draw my four quarters better.

03:26 Okay.

03:29 So we'll look at faraday's law of induction and in its qualitative form states that the potential difference.

03:57 I'm going to abbreviate a little bit.

03:58 This is a long one.

03:59 It's induced in a loop when the number of magnetic fields, field lines passing through the loop changes with time.

04:52 So we're going to count the field lines passing through the loop when the loop just enters the region of the magnetic field.

05:06 Okay...

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