Use Lenz's law to answer the following questions concerning...

Use Lenz's law to answer the following questions concerning the direction of induced currents. (a) What is the direction of the induced current in resistor $R$ in Figure P31.28a when the bar magnet is moved to the left? (b) What is the direction of the current induced in the resistor $R$ immediately after the switch $\mathrm{S}$ in Figure $\mathrm{P} 31.28 \mathrm{b}$ is closed? (c) What is the direction of the induced current in $R$ when the current $I$ in Figure $\mathrm{P} 31.28 \mathrm{c}$ decreases rapidly to zero? (d) A copper bar is moved to the right while its axis is maintained in a direction perpendicular to a magnetic field as shown in Figure P31.28d. If the top of the bar becomes positive relative to the bottom, what is the direction of the magnetic field?

Key Concepts

Right-Hand Rule

The right-hand rule is a mnemonic device used to determine the direction of induced current or magnetic forces. When applied in the context of electromagnetic induction, it helps predict the direction in which current flows in order to oppose the change in magnetic flux, in accordance with Lenz's Law.

Lenz's Law

Lenz's Law states that the direction of an induced current in a circuit is such that the magnetic field created by the induced current opposes the change in the original magnetic flux that produced it. This principle is a manifestation of the conservation of energy and is fundamental in determining the behavior of systems under electromagnetic induction.

Magnetic Flux

Magnetic flux is defined as the product of the magnetic field and the area through which the field lines pass, oriented perpendicular to the surface. Changes in magnetic flux, whether through variations in the field strength, the area, or the orientation of the surface, are what induce an electromotive force (EMF) in a circuit.

Faraday's Law of Electromagnetic Induction

Faraday's Law relates the induced electromotive force in a circuit to the rate of change of magnetic flux through the circuit. It provides the quantitative basis for electromagnetic induction, establishing that any change in the magnetic environment of a coil of wire will create an induced voltage.

Transcript

00:01 Hello and welcome to this video solution of numerate so here using lens law you have to answer the following question a what is the direction of the induced current in the resistor? r as per this diagram right and here you see that there is a magnet having not south pole which is moving away from it, right? so this is a so here you have to understand that if you're moving away then the magnetic field intensity over it decreases, right? now the magnetic field intensity will be directed if you see it starts from north and end towards the south, right? kind of like this so since the north pole is moving away, then the magnetic field intensity reduces so a current has to be induced so as to produce a magnetic field towards the left side, right? sorry towards the right side because the north pole produces magnetic field towards the right kind of like this right so here and if you see there will be a current which is directed from left to right in the resistor, right? it will be counterclockwise if you are viewing from this side, right? if you are viewing from this side, then it will be counterclockwise and there will be there in the resistor their current will from left to right and on the other side in the second part what is the direction of the induced current in the resistor are after the switch is closed now, right when the switch is closed? there will be current moving in the coil, right? now as per lenz's law current will be induced was to reduce the current, right? because suddenly there is a lot of current passing through this solenoid, let's say and so and if you see the direction of current just let me have a look.

02:18 Yeah, it's sort of like this that is if you are viewing from again from this side view then it will be clockwise, right? so clockwise direction produces a current magnetic field to the left.

02:32 So there will be a reverse current which is in the counterclockwise direction that will produce current to the magnetic field to the right, right so a clockwise current will be produced so as to take it from left to right again in the resistor, right? left to right next see here.

03:06 You have got coil or circuit this is our and here you have got a current carrying wire, right? now here the current is rapidly decreased to zero that means if you see here the magnetic field produced into this coil will be into the plane if you apply right hand thumb rule you have to place your thumb along the direction of the current and rotate your finger so it's into the plane right now it when it is decreased to zero then this intensity is reducing, right? so there will be a current in this resistor so as to increase the effect, right? so clearly a clockwise current has to be produced right that will produce extra electric magnetic field into the so here again, it's from left to right the last one is d here you it's given that there is a rod or bar that is moving to the right v and it is given that charges positive charges are developed at the top and negative charges in the bottom, right and actually, this is the concept of motion a liam affair this bar will be acting like a battery right and inside the battery charges move from negative to the positive that means in the upward direction right...

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