A circular loop of wire is in a region of spatially uniform...

A circular loop of wire is in a region of spatially uniform magnetic field, as shown in Fig. E29.15. The magnetic field is directed into the plane of the figure. Determine the direction (clockwise or counterclockwise) of the induced current in the loop when (a) $B$ is increasing; (b) $B$ is decreasing; (c) $B$ is constant with value $B_{0}$. Explain your reasoning.

Key Concepts

Magnetic Flux

Magnetic flux is a measure of the quantity of magnetic field passing through a given area. It is affected by both the strength of the magnetic field and the orientation of the area relative to the field direction. Changes in magnetic flux are central to understanding electromagnetic induction, as they lead to the generation of an electromotive force (EMF) in a loop of wire.

Faraday's Law of Induction

Faraday's law states that a changing magnetic flux through a circuit induces an electromotive force (EMF) in the circuit. The magnitude of this induced EMF is proportional to the rate of change of the magnetic flux. This principle is fundamental in the study of how electric currents can be generated by changing magnetic fields.

Lenz's Law

Lenz's law provides the direction of the induced current resulting from a change in magnetic flux. It states that the induced current will flow in such a direction that its own magnetic field opposes the change in the original magnetic flux. This concept is key in predicting whether the induced current will be clockwise or counterclockwise in various situations of increasing or decreasing magnetic fields.

Right-Hand Rule

The right-hand rule is a mnemonic used to determine the direction of the induced current or the magnetic field in electromagnetic situations such as those described by Faraday's and Lenz's laws. By aligning the thumb and fingers appropriately, one can visualize the orientation of the induced current in relation to the applied magnetic field, aiding in the prediction of current direction in a loop.

Transcript

00:02 Okay, so before we talk about the direction of the current, we need to understand that when will have some non zero current.

00:12 So, as you can see, you haven't uniform and netted field, and then you have a circular dupe.

00:18 Now we need to understand that if the magnetic field is changing on lee, then we'll have some non zero current.

00:27 So if you look at the problems, we have three different sections where you have bees increasing b is decreasing and b's constant.

00:36 So we can easily say that if these constant there's no induced currents, so are in india's current will.

00:45 Be zero there's.

00:46 But then let's talk about the first part where your magnetic field is increasing.

00:52 So as you can see, your magnetic field is pointing towards the page.

00:56 And, ah so so let's let's figure out how to find out the direction.

01:02 So remember that we have some increasing current.

01:09 Sorry, andi, remember, we have some increasing magnetic field.

01:12 So now we have to look at lenz's law, which tells us that if there is some changing current, the sankara luke will try to oppose the fact.

01:24 So basically your magnetic field is increasing towards the page.

01:29 So there will be some opposing magnetic field which will be outside, which will be pointing towards us.

01:37 Right? so let's actually mark those.

01:42 So it's a these will be the magnetic fields that are pointing towards us.

01:51 Right? so now we know that these are the magnetic fields that that's being induced because we're because our bees increasing.

02:02 So if we know that, ok, our magnetic field is pointing towards us, we can use our right and rule...

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