00:01
Okay, so in this problem, you have a coil of wire that has 50 turns in a magnetic field.
00:05
That magnetic field is oriented perfectly perpendicular to the coils, and its magnitude is changing over time.
00:12
The magnitude of magnetic field in any given time is given by the equation b equals 0 .04 t squared plus 0 .07t plus 0 .168, where t is the time in seconds.
00:26
The diameter of each loop of this coil is 12 .5 centimeters, and again, you're asked to find the induced emf at time equals 1 .95 seconds.
00:36
So to go about time with this problem, the first thing you're going to want to do is find the flux enclosed by the coil at the initial and final time.
00:44
And the flux represented by fee is equal to the strength magnetic field times the area enclosed.
00:51
So the area enclosed is just going to be the area enclosed by one loop with this coil.
00:54
So that's just a circle.
00:56
The area of a circle is pi r squared.
00:59
In this case, our r is half of the 12 .5 centimeter diameter, but we'll do this in meters.
01:05
So we'll say 0 .125 meters divided by 2.
01:11
And if you carry this calculation out, you'll find that a is approximately 0 .0123 meters squared.
01:20
So now you have your a.
01:25
Of the magnetic field at both times, you just need to plug t into this equation up here.
01:30
So at time zero, you can see this term and this term are going to be equal to zero because you're multiplied by t.
01:36
So you're left with a b initial is just 0 .168.
01:43
And then at the final time, we're going to have to plug 1 .95 in for t...