In Fig. E29.25 a conducting rod of length L=30.0 cm moves in a magnetic field B of magnitude 0.

step 1 in the given problem here. This is a uniform magnetic field which is directed into the plane of

In Fig. E29.25 a conducting rod of length L=30.0 cm moves...

Key Concepts

Motional EMF

Motional electromotive force (EMF) is the voltage generated across a conductor when it moves through a magnetic field. This phenomenon is quantitatively described by the relation EMF = B * L * v (where B is the magnetic field strength, L is the length of the conductor, and v is its velocity perpendicular to the field), illustrating how the interplay of magnetic fields and motion leads to electrical energy production.

Magnetic Field

A magnetic field is a region of space where a magnetic force is experienced by moving charges or magnetic dipoles. In physics, it is described by both a magnitude and a direction, and it influences charged particles by exerting a force perpendicular to their velocity, which is essential for understanding how motion in these fields can induce electrical effects in conductors.

Motion of Conductors

When a conductor moves through a magnetic field, its free charges (electrons) experience forces that can separate positive and negative charges, creating an electric potential difference across the conductor. This movement underlies many electromagnetic induction phenomena and is a cornerstone of how mechanical motion is converted into electrical energy.

Lorentz Force

The Lorentz force is the force exerted on a charged particle moving within electric and magnetic fields. For a moving conductor, this force acts on the electrons, causing them to accumulate at different ends of the rod, which is the fundamental mechanism that gives rise to motional EMF. This concept is critical in linking the mechanical movement of conductors and the resulting electromagnetic effects.

Transcript

00:01 In the given problem here.

00:02 This is a uniform magnetic field which is directed into the plane of paper perpendicularly.

00:15 And within this magnetic field there is a straight rod named as ab which is moving in this magnetic field like this.

00:28 In the direction of this arrow.

00:32 Length of this rod is given as 30 .0 centimeter, or we can say this is 0 .30 meter.

00:43 The magnetic field directed into the plane of paper is having a magnitude of 0 .450 tesla and the speed with which it is moving perpendicular to these magnetic field lines, is given as 5 .00 meter per second.

01:04 Now, in the first part of the problem, we have to find the motional emf induced across the ends of this rod, and that is given as epsilon is equal to bv, the product of magnetic field, and speed of the rod, and length of the rod.

01:39 And plugging in unknown values, this is 0 .450 tesla into 5 .00 meter per second multiplied by length of the rod, which is 0 .30 meter.

01:57 And finally, this emf induced comes out to be 0 .67 volt.

02:04 And it becomes the answer for the first part of the problem.

02:10 Now, in the second part of the problem, we have to find the direction of current induced in this rod.

02:21 So using lemming's right hand rule, we conclude that the direction of current in this rod is from a to b.

02:59 And we know in case of motionally emf, the current always passes through a conductor from low potential to high potential.

03:12 Hence we conclude here and b of the raw is at a high potential.

03:33 In the third part of the problem, we have to find magnitude and direction of electric field induced across the ends of this raw.

03:43 So the magnitude of electric field will be given as potential gradient, means the gradient of emf induced, epsilon by l.

04:02 So it becomes 0 .675 volt divided by length of the conductor, which was 0 .m...

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