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 $R$ shown in Figure $\mathrm{P} 31.26 \mathrm{a}$ when the bar magnet is moved to the left? (b) What is the direction of the current induced in the resistor $R$ right after the switch $\mathrm{S}$ in Figure $\mathrm{P} 31.26 \mathrm{~b}$ is closed? (c) What is the direction of the induced current in $R$ when the current $I$ in Figure $\mathrm{P} 31.26 \mathrm{c}$ 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 $\mathrm{P} 31.26 \mathrm{~d}$. If the top of the bar becomes positive relative to the bottom, what is the direction of the magnetic field?

Key Concepts

Magnetic Flux

Magnetic flux is a measure of the total magnetic field that passes through a given area. It is a key concept in electromagnetism because changes in magnetic flux are what induce currents in conductors according to Faraday’s law. Understanding magnetic flux is essential for analyzing how external magnetic fields interact with electrical circuits.

Faraday’s Law

Faraday’s law quantitatively describes electromagnetic induction by stating that the induced electromotive force (emf) in a closed circuit is proportional to the negative rate of change of magnetic flux through the circuit. This relationship connects changes in magnetic environments to the voltages generated in conductors, thereby linking magnetic fields and electric currents in dynamic systems.

Right-Hand Rule

The right-hand rule is a mnemonic that helps determine the direction of the induced current or the magnetic field in electromagnetism. It is used to relate the direction of motion, magnetic field, and resultant force or current, thereby providing a systematic way to predict the behavior of charges in magnetic fields.

Lenz’s Law

Lenz’s law is a principle that explains the direction of an induced current in a conductor when the magnetic flux through the conductor changes. It states that the direction of the induced current is such that its own magnetic field opposes the change in the original magnetic flux. This opposition ensures the conservation of energy and is fundamental in predicting how systems respond when subjected to a changing magnetic field.

Electromagnetic Induction

Electromagnetic induction is the process by which a time-varying magnetic field produces an electromotive force in a conductor. This phenomenon underlies the operation of many electrical devices, such as generators and transformers, and is described quantitatively by Faraday’s law. It forms the basis for understanding how induced currents arise in circuits exposed to changing magnetic conditions.

Transcript

00:02 Hi, in the first part of the given problem, this is a solenoid having a large number of turns of a conducting wire wound over the core.

00:24 This is a resistance attached with the coil, resistance r, points a and b.

00:37 It has been given that a bar magnet is moving away from this solenoid such that the north pole of the bar magnet is going away as the reason behind the emf induced in this solenoid will be going away of this north pole and the magnetic field lines come out of the north pole so as the north pole will move away from the left end, the solenoid, the magnetic flux passing through this left end will change due to the change in this magnetic flux, an emf will be induced in the left face of this solenoid.

01:35 And as per lenses law, the nature of this emf induced will be such that the magnetism induced due to that induced emf will be such that it will oppose the reason behind its induction.

01:50 So as the reason is going away of the north pole, so the direction of current induced in the left end of the coil should be such that the left end, the left face of the coil, should start behaving like south pole, so that it may attract the north pole of the bar magnet which is going away from it.

02:13 So as north pole, of the magnet is going away from the left face of the solenoid.

02:46 The direction of current induced in it should be such that this face may behave like south pole, which will attract the north pole.

03:35 Going away from it.

03:42 So the current induced should be in clockwise direction in the left face.

04:01 It should be in the clockwise direction means to say like this and if the direction of current in the left face is clockwise so it will be getting down to point and then will pass through the resistance from a to b.

04:22 So the direction of current induced in the left face should be from a to b...

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