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[Solved] Estimate induced emf in the coil
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.
emf = -N*(change in flux)/change in time
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 textbook 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.
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 textbook 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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