A small, circular ring is inside a larger loop that is...

A small, circular ring is inside a larger loop that is connected to a battery and a switch ($\textbf{Fig. E29.21}$). Use Lenz's law to find the direction of the current induced in the small ring (a) just after switch $S$ is closed; (b) after $S$ has been closed a long time; (c) just after $S$ has been reopened after it was closed for a long time.

Key Concepts

Electromagnetic Induction

Electromagnetic induction is the phenomenon by which a changing magnetic field within a closed loop induces an electromotive force (emf) and consequently an electric current in that loop. This principle is the basis for the operation of many electrical devices and is central to understanding how varying fields affect nearby conductors.

Faraday's Law

Faraday's Law quantitatively describes the process of electromagnetic induction, stating that the induced emf in a closed loop is proportional to the rate of change of magnetic flux through the loop. This law is essential for calculating how variations in magnetic fields produce measurable electrical effects, serving as a bridge between magnetic phenomena and electrical response.

Lenz's Law

Lenz's Law provides the direction of the induced current resulting from electromagnetic induction, asserting that the induced current will flow in a direction that opposes the change in magnetic flux that produced it. This fundamental law ensures the conservation of energy by counteracting the initial disturbance in the magnetic field.

Magnetic Flux

Magnetic flux is defined as the total magnetic field passing through a given area, and it plays a vital role in electromagnetic induction. The change in magnetic flux through a conductive loop is what drives the induced emf and current, making it a key parameter in understanding and analyzing induced effects.

Transient and Steady-State Response in Circuits

When a circuit is subject to sudden changes, like closing or opening a switch, it exhibits a transient response before settling into a steady state. The transient phase involves rapidly changing currents and magnetic fields, which can induce additional currents in nearby conductors. Understanding both transient behavior and steady-state conditions is crucial for accurately predicting how induced currents will behave over time in response to changes in the circuit.

Transcript

00:01 Okay, so we're doing chapter 29, probably 21.

00:05 And this has a figure here.

00:07 We have a circular loop that's surrounded by another bigger circular loop that is connected to a battery.

00:16 And this battery is connected to a switch.

00:19 We call that switch s.

00:22 Okay.

00:23 So we want to use linz's law to figure out the direction of the current that is reduced in the small ring in the middle here.

00:33 Okay, so let's first imagine when the switch is closed, we have a current around that's flowing around counterclockwise.

00:44 So with s close, i is counterclockwise.

00:55 So b is using the right hand rule out of the page.

01:04 Okay, so part a asks us to figure out.

01:10 The direction of the induced current just after the switch is closed.

01:15 Since we start with an initial current of zero with the switch open, the change in current is greater than zero.

01:23 So the bdt is greater than zero, which means the change influx greater than zero, and that means it is out of the page and increasing.

01:41 So to oppose that, linz's law says the current induced must induce a b field or make a b field into the page.

01:56 Sorry, this dot is out of the page.

01:59 So the changing is out of the page and increasing.

02:01 So the induced current must oppose that by making a b field into the page.

02:07 So b induced is into the page...

Please give Ace some feedback