A circular loop of wire with radius r 00480 m and resistance...

A circular loop of wire with radius $r =$ 0.0480 m and resistance $R =$ 0.160 $\Omega$ is in a region of spatially uniform magnetic field, as shown in $\textbf{Fig. E29.22}$. The magnetic field is directed out of the plane of the figure. The magnetic field has an initial value of 8.00 T and is decreasing at a rate of $dB/dt =$ -0.680 T>s. (a) Is the induced current in the loop clockwise or counterclockwise? (b) What is the rate at which electrical energy is being dissipated by the resistance of the loop?

Transcript

00:01 Here we're looking at an example that we will need faraday's law of induction.

00:07 So faraday's law of induction tells us how we may create a voltage or an emf by changing a magnetic flux.

00:19 That emf is minus n, the number of loops, times the change in magnetic flux with time.

00:30 Here we are looking at a single loop, so n is equal to 1.

00:37 The negative sign is related to the concept of lentz's law, and will give us the direction of the induced emf.

00:51 What is magnetic flux? magnetic flux is a product of a magnetic field, vector, dot product into an area that you either imagine enclosed or there is an actual loop there enclosing it.

01:11 Here, the area and the magnetic field are aligned, so we do not need the dot product.

01:17 We can simply write it as b times area.

01:23 In our instance, it is the magnetic field that's changing in time, not the area of the loop.

01:29 And so our emf, i will say absolute magnitude, is equal to the area times the absolute magnitude of the change in the magnetic field in time.

01:45 So we are told that that change is a decrease.

01:50 What we can do with that understanding that it is a decrease is we can determine the direction of induced current that flows through a resistive.

02:01 Loop that has its area vector parallel to the magnetic field.

02:08 What we know by lentz's law is that the loop of wire will try to oppose the change, which is a decrease.

02:19 So what that wire will try to do is create an induced magnetic field parallel to the outside external magnetic field.

02:31 Which means it will point out of the page.

02:35 Then using your right -hand rule and wrapping your fingers around that loop of your right hand, that is, you find that the current, induced current, has to flow in a counterclockwise sense.

02:53 So that is the direction of the current.

02:56 Let's now figure out the amount of the induced emf.

03:01 We will need the area of the loop...

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