WEBVTT
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for part A were asked to find a symbolic expression
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for the induced IMF and the coil in terms of
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the variables that are given so well indicate this is
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part of a So the induced e m f is
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equal to the number of turns in the coil multiplied
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by the magnitude of the changing magnetic flux. I
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felt if I divided by the change in time,
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felt a t so this is equal to the number
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of turns multiplied by. Well, the area of
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the coil is not gonna change right. The only
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thing that's changing is the magnetic field from the initial
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to the final. So this is the final magnetic
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field multiplied by the area, multiplied by the co
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sign of the angle. Fada minus be initial multiplied
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by the area multiplied by the same angle coastline data
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all divided by Delta teak. So all that's over
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felt a T Well, we're told here that the
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final magnetic field is equal to be not. We're
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told that initially the magnetic field is equal to zero
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. Based upon the setup of the problem, Veda
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is equal to zero degrees. We're told that the
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time that transpires is just time t so Delta t
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here it's just equal to t. So therefore,
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the induced e m f is going to be equal
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to the number of turns. Times be zero,
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right? Because the initial zeros that expression goes away
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, That part goes away. The area is pi
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r squared since it's circular and then co sign of
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zero is one. So we can just ignore that
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term. And this is all divided by t.
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So this is our expression for the induced in meth
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and we can go ahead and box it in Is
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their solution for part A for part B, it
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says looking down on the X Y plane from the
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positive Z access is the direction of the induced current
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clockwise or is it counterclockwise? Okay, so the
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direction of the magnetic field is upwards, which is
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the positive ZY direction. The coil is viewed from
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the positive Z access. So in this case,
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the current induced in the coil must appear to be
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the in a clockwise direction. This is because the
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magnetic field is increasing in the positive direction and due
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to which the link magnetic flux also directed in the
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positive dpz direction. So to oppose this flux,
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the induced current should produce the magnetic field in a
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downward direction or the negative Z direction. Therefore,
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the induced current must flow in a clockwise direction.
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So for part B, we can say that the
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magnetic field is in the Z hat direction. Therefore
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, the, um therefore, the induced current must
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flow in a clockwise direction. So thus we can
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say thus induced current in clockwise direction. We can
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go in and box that in as our solution for
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part B. Okay, Now, for part C
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were told that if each loop has a resistance,
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are finding expression for the magnitude of the induced current
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. Okay, well, the induced current I is
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equal to the induced at the M f divided by
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the resistance. We're gonna call this our prime,
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and we're told that our prime is equal to the
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number of terms times the resistance in each turn.
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Okay, So, plugging that value into this expression
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, we find that I concert this down just a
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little bit more so we have some more room.
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We find that I is equal to what we,
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uh the induced e m f which we found on
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the first page to be the number of turns times
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B zero times pi r squared, divided by time
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But of course, the number of turns are gonna
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cancel out because our prime also has the same number
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of turns in it. So we're left with an
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expression that's be zero times pi r squared, Okay
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. Divided by the time that transpires t multiplied by
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the resistance in each turn are we can go ahead
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and box set in as our expression for the current
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in the answer for part C.