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Looking through some old exams i found this problem where im supposed to derive an expression for the induced emf, ${\mathcal {E}}$(t), of a square loop moving into an homogenous magnetic field and then find the maximum value

enter image description here

Now the thing im unsure of is how the area changes with time. The thing that is throwing me off is the fact that it comes in at an angle. Like if it was standing straight it wouldnt be a problem but does the fact that its angeled change anything?

How would i go about setting up formula for the changing area?

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  • $\begingroup$ You might want to start by noting that the shape made by the loop as it enters forms a triangle (at least for the first half of the shape) $\endgroup$
    – Triatticus
    Commented Feb 3, 2020 at 23:37

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If I were you, I would assume that the angle is 45 degrees like the picture seems to show, and also that the boundary of the region with the magnetic field is sharp. Then you would need to break the area function $A(t)$ into two cases, before and after the middle of the loop has entered the magnetic field.

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  • $\begingroup$ It will be area of a triangle plus the area of a trapezoid, since the second triangle comes in backward. Also there isn't any reason to subdivide the first triangle as it's area will just be base times height. $\endgroup$
    – Triatticus
    Commented Feb 4, 2020 at 0:11

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