A wire loop consists of two equal parts that are connected...

A wire loop consists of two equal parts that are connected so that they form a "rectangular figure eight." The loop is moving with constant speed through a region of uniform $\vec{B}$ field that points into the page (Figure $P 21.42$ ). The longer side of the loop is twice the width of the magnetic field region. Draw a qualitative graph that shows how the induced current in the loop depends on time during the period in which the loop moves from the position shown in the figure to the position where the left side of the loop exits the magnetic field. Assume that a counterclockwise direction of the current in the right half of the loop is positive.

Key Concepts

Electromagnetic Induction

Electromagnetic induction is the process by which a changing magnetic environment generates an electromotive force (EMF) in a conductor. This concept is fundamental in understanding how motion or a change in the magnetic field around a circuit can produce an electrical current.

Magnetic Flux

Magnetic flux quantifies the amount of magnetic field passing through a given area and is calculated as the product of the magnetic field strength, the area through which the field lines pass, and the cosine of the angle between the field and the area’s normal. In problems involving moving loops, variations in the flux through the loop generate changes that are central to inducing an EMF.

Faraday’s Law

Faraday’s Law of electromagnetic induction states that the induced electromotive force in any closed circuit is equal to the negative rate of change of the magnetic flux through the circuit. This principle explains how any time-varying magnetic field, whether due to movement of the loop or changes in the field strength, leads to an induced EMF.

Lenz’s Law

Lenz’s Law provides the direction of the induced current resulting from electromagnetic induction. It states that the induced current will flow in a direction such that its own magnetic field opposes the change in the original magnetic flux. This opposition helps to conserve energy and is crucial for determining the current’s sign in circuits undergoing flux changes.

Motional EMF

Motional EMF refers to the voltage induced in a conductor moving through a magnetic field. When portions of a circuit move relative to a magnetic field, the charges in the conductor experience a magnetic force, which creates a potential difference across the conductor, leading to an induced current.

Transcript

00:02 Hi, in the given problem here this is a uniform magnetic field directed into the plane of paper perpendicularly and having a linear expansion up to a distance of d.

00:24 Then a rectangular coil is entering into this magnetic field perpendicularly.

00:34 This magnetic field is twist here this coil is twisted after half of its length such that its orientation will be reversed for the next half length so this combined length becomes twice of d when it is entering into the magnetic field with a speed v it will take a time t1 is equal to d by v to enter into the field up to half of its area and further time t will be taken by the coil to come out of the magnetic field with the same velocity moving with the same constant velocity so now we have to plot a curve between the current induced and the time taken taking the direction of current which is counterclockwise as positive.

01:47 So here take the current over y -axis and we take the time over x -axis.

01:52 So in the first half motion of this coil, as the reason behind the emf induced or current induced is the magnetic field which is in a direction inward into the plane of paper and as the coil is moving into the magnetic field, this magnetic field is increasing.

02:13 So the reason is inward increasing magnetic field.

02:21 So its opposition should be, as per lenz's law, outward increasing magnetic field.

02:35 And as we know, the magnetic field comes out of a north pole only.

02:41 So this face of the coil, the right half of the coil should start behaving like north pole.

02:47 So the direction of current induced, it should be counter clock wise.

02:56 And here we take the time d by v as t1 and the further time it will become 2d by v.

03:03 And for this time, the current induced is shown here, whatever the value it may have, we don't know anything about the value of the current induced...

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