A 0.650-m -long metal bar is pulled to the right at a steady 5.0 m / s perpendicular to a unifo

step 1 for the first item off. This question we use for it is law which states that induces electro mot

A 0.650-m -long metal bar is pulled to the right at a steady...

A $0.650-\mathrm{m}$ -long metal bar is pulled to the right at a steady $5.0 \mathrm{~m} / \mathrm{s}$ perpendicular to a uniform, $0.750 \mathrm{~T}$ magnetic field. The bar rides on parallel metal rails connected through a $25.0 \Omega$ resistor (Fig. $\mathbf{E} 29.28),$ so the apparatus makes a complete circuit. Ignore the resistance of the bar and the rails. (a) Calculate the magnitude of the emf induced in the circuit. (b) Find the direction of the current induced in the circuit by using (i) the magnetic force on the charges in the moving bar; (ii) Faraday's law; (iii) Lenz's law. (c) Calculate the current through the resistor.

Key Concepts

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 such a direction that its own magnetic field opposes the change in the magnetic flux that produced it. This principle ensures the conservation of energy and is crucial for determining the polarity of the induced EMF in a circuit.

Ohm's Law

Ohm's Law relates the current flowing through a conductor to the voltage across it and the resistance of the conductor. It provides a simple linear relationship where the current is equal to the voltage divided by the resistance. This law is essential for calculating the induced current in a circuit once the EMF and resistance are known.

Magnetic Force on Moving Charges

The magnetic force on moving charges, described by the Lorentz force law, explains the force experienced by charge carriers moving within a magnetic field. This force is perpendicular to both the velocity of the charge and the magnetic field, and is the cause of charge separation in a moving conductor that leads to the creation of motional EMF. Understanding this concept is key to analyzing how currents are induced in conductors moving through magnetic fields.

Magnetic Flux

Magnetic flux is a measure of the total magnetic field passing through a given area. It is dependent on the strength of the magnetic field and the orientation and size of the area through which the field lines pass. An understanding of magnetic flux is essential for applying Faraday's Law, as the induced EMF is directly related to the rate of change of magnetic flux through a circuit.

Faraday's Law

Faraday's Law of electromagnetic induction states that the induced electromotive force in a closed circuit is equal to the negative rate of change of the magnetic flux through the circuit. This law connects the concepts of magnetic flux, time-varying magnetic fields, and induced currents, and provides the fundamental principle behind how changing magnetic environments can induce electrical currents in conductors.

Motional EMF

Motional EMF refers to the electromotive force generated when a conductor moves through a magnetic field. This phenomenon occurs due to the magnetic Lorentz force acting on the charge carriers within the conductor, which leads to a separation of charges and an induced voltage. The magnitude of the induced EMF is directly proportional to the velocity of the conductor, the strength of the magnetic field, and the length of the conductor within the field.

Transcript

00:01 For the first item off.

00:01 This question we use for it is law which states that induces electro motive force is given by minus that derivative off the flux of magnetic field with respect to time.

00:13 The area that we have to use them for these law is this area is the area off the circuit, and that area is changing because this part of the circuit is moving to the right.

00:24 Then we can calculate the flux as follows.

00:27 The flux off magnetic field is given by the integral off d a, which is an area element times the magnetic field.

00:36 Be now notice the following the orientation off that surface a is given by your vector that is normal to the surface.

00:47 A factor that is normal to the surface is a factor that is pointing either our ports or in words.

00:53 We can choose the orientation of that factor.

00:56 It is conventional to choose, eat as pointing outwards.

01:00 So the vector e should be something like this.

01:06 Then i'm going with this convention.

01:09 The reform.

01:09 You can see that a and b are untie parallel so we can write it as minus the integral off d a times be where now we are working with magnitudes the magnitude of the magnetic field is constant so we have miners b times the integral off the a which is just the area.

01:31 So the flux is minus b times a the area off that rectangle is given by the product off its size.

01:39 So the flux is my news.

01:40 Be times l which is these side times is more l which is disorder site now we can take the derivative respect time to get the following mine has been times l they are constant times the l divided by the teeth the ltte is the reach off change off l which is the same as the velocity off this bar search results in minus b times l a times we there afford induce it e n f is minus minus beat lv which results in b times l a times.

02:21 We therefore plugging the numbers we get 0.75 times 0.65 times five, which results in an e m f off 2.4375 which can be rounded to 2.4 votes.

02:40 And this is the answer to the first item before proceeding.

02:43 Let me clear my board.

02:45 Okay.

02:46 The second item has three super items in all of them.

02:49 We have to do to remind what is the direction of the current, but using different methods, the first item would have to use the magnetic force that is acting on the current.

03:00 So you let us suppose that there is a charge seating right here? discharge is a charge q.

03:07 Then the magnetic force acting on these charge is given by cube times v cross beat.

03:18 We can see that in the situation v is pointing to the right while b is pointing inside the board like this...

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