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**[Solved] Estimate induced emf in the coil**

## Homework Statement

Consider a single-loop coil whose magnetic flux is given by this image:

Estimate the induced emf in the coil at times near t = 0.3s, t = 0.4s and t = 0.5s

This is for algebra-based physics.

## Homework Equations

emf = -N*(change in flux)/change in time

## The Attempt at a Solution

At t = 0.3s

emf = -1(4- -4)/(0.4 - 0.2) = -8/0.2 = -40V

At t = 0.4s

Rate of change = 0

At t = 0.5s

emf = -1(-4 - 4)/(0.6 - 0.4) = 8/0.2 = 40V

My first and third answers are wrong. What've I missed? The text book has -0.06kV, 0 and 0.06kV but those answers are also incorrect.

**Edit:**Solved it. This is the graph of

4 Cos[(2 Pi/(0.4))*x]

Differentiating this gives y = -20pi*Sin[5pi*x]

Evaluating it at t = 0.3 s gives 63V. I do not know why differentiation is used for an algebra-based physics problem when my TA explicitly told me to not use calculus, but there it is.

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