A single loop of wire with an area of 0.0900 m^2 is in a uniform magnetic field that has an init

A single loop of wire with an area of 0.0900 m^2 is in a...

Key Concepts

Ohm's Law in the Context of Induced Currents

Ohm's law relates the voltage (or emf) across a conductor to the current flowing through it and its resistance. When an emf is induced in a loop due to a changing magnetic flux, the resulting current can be determined by dividing the induced emf by the resistance of the loop. This relationship is essential for analyzing circuits where induced currents occur.

Faraday's Law of Electromagnetic Induction

Faraday's law states that an electromotive force (emf) is induced in a circuit when the magnetic flux through the circuit changes over time. The magnitude of the induced emf is equal to the rate of change of the magnetic flux, with a negative sign indicating the direction of the induced emf opposes the change in flux. This law is fundamental in explaining how electric generators and many other devices work.

Magnetic Flux

Magnetic flux represents the amount of magnetic field passing through a given area. It is calculated as the product of the magnetic field strength, the area it penetrates, and the cosine of the angle between the field direction and the normal to the area. This concept is crucial for understanding how changes in the magnetic environment can lead to induced effects in conductive loops.

Transcript

00:01 Okay, aloha.

00:03 We're going to be solving a problem from sears and romance keys textbook in chapter twenty nine.

00:09 Section two can't problem one.

00:12 We're told that there is a single loop of wire with an area which i call a, which is zero point zero nine zero zero meter square, and we're told that there's a magnetic field that's perpendicular to lou.

00:38 So ana and then we're also told that the value of magnetic field there is three point eight euro tesla's and that's its initial value, its values decreasing at a rate of zero point one nine, tesla's per second and i'm going to a label this rate of change dpt.

01:13 It's decreasing zits negative.

01:22 And we're told this we're asked to find the imf electra motive force induced in this loop.

01:32 So to solve this problem, we're going to have to use faraday's law of induction and that lawson rise in exhibition where e, which is three electoral, would've forced deena.

01:51 You go to the rate of change of the flux which you call fi, and we're going to use this libation to solve part of this problem, which is to find the imf induced.

02:08 So you can write this out as this e is minus defy no use like the textbooks, a subscript b for magnetic field team and the first part oh, going to solve to solve this problem is to calculate five b.

02:30 This is the magnetic flux influx you could think of as almost like imagining a fluid going down type.

02:38 This is how much pain yet it feels flowing through that loop, and we calculate that by doing and nature over the area of the loop.

02:52 Well, we do the magnetic field come and it stopped product with that area.

02:57 We're doing interest some of the area, and because the direction the area is the direction that's coming out of the loop, it's normal to the cross sectional area of the loop.

03:09 So the angle between the magnetic field in that direction is zero, so we can alternately, right.

03:18 This stop product is b d.

03:20 A times co.

03:23 Sign zero.

03:27 That's the angle between b and d a, which is he was a one.

03:32 And because we know that bee is uniform, we can also take be out of the central of the area.

03:37 It's not changing across the loop, and then we would just have an integral left over the area.

03:46 But this is that's just the total area a which were given in the problem.

03:53 So that's five b and then we need to calculate defi b t t to get it.

04:01 Our answer to the question about the emma solving that over here subscript b.

04:14 It's going to be the time derivative of what we just calculated, which is b times a you know, wait a could change if is...

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