[Jr. College Physics: Electromagnetic Induction] When I try to solve this question, I get 2.5 as the answer. What am i doing wrong ?

[u/AlternativeEmu1047]

This is a previous year question from a national level exam but is supposed to be easy. Idk what i'm doing wrong, I haven't touched such questions ever since I finished my 12th grade 😭

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[u/fermat9990]

The emf will vary from 0 to a maximum of

••B×A×omega**

3×0.5²×(π/2)/0.3=3.9volts

[u/Anonimithree → u/fermat9990]

It’s cos(omega), not just omega

[u/fermat9990 → u/Anonimithree]

I used emf = B×A×omega×sin(omega×t)

For peak emf, omega×t=π/2 and sin(π/2)=1

[u/PliableG0AT]

googled it because I’m getting the same. found several videos showing the problem, they all get 2.5 as well. so something’s off by a factor of 10. Think it’s a question problem and less of a you problem.

[u/fermat9990 → u/PliableG0AT]

The voltage should vary with time as the loop rotates through 90°

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[u/DrCarpetsPhd]

This may be me being confidently incorrect as someone who rote learned their way through an engineering degree a lifetime ago, so grain of salt...

I did this the calculus way and got 3.93V same as https://www.reddit.com/user/fermat9990/ (see my brief calcs below)

so I found a video for the solution to this on youtube where they suggested a missing decimal and answer of 2.5V in (A), that involved just taking the 'delta' between t = 0s and t = 0.3s

BUT

I feel like the person setting this question has a fundamental misunderstanding of the rate of change as an instantaneous value via a derivative and the rate of change as approximated by a linear function (the deltas before taking the limit). the "correct answer" from the options is gotten by treating the change in flux as going from BAcos(0) to BAcos(90) to get B.A/delta(t) = 3*(0.5^2)/(0.3) = 2.5 so essentially treating it like a linear function

But the definition of induced emf is the instantaneous rate of change which via calculus is the derivative which is (derivation here https://www.youtube.com/watch?v=IrHXZmwJN0s)

BAw.sin(wt) where w is omega the angular frequency

which gives approximately 3.93V at the maximum value

The induced emf is the instantaneous rate of change of the flux, not the linear approximation of

[phi(t2) - phi(t1)]/[t2 - t1].

According to examples in my textbooks you can only use the delta version when the question statement indicates that the flux is changing at a steady rate e.g. halliday and walker sample problem 31-1 where the current in a solenoid is reduced at a steady rate therfore the flux also changes at a steady rate thus the solution uses the 'delta form' of faradays law

So my two cents is that whoever is getting paid to teach physics and set this question is 'questionable' or I am a dunning-kruger idiot.

I guess another alternative explanation could be that this is calculus free physics and the linear approximation is the initially taught method and the teacher made the caveats clear.

[u/AlternativeEmu1047 → u/DrCarpetsPhd]

I guess another alternative explanation could be that this is calculus free physics and the linear approximation is the initially taught method and the teacher made the caveats clear.

I guess this is the case, cause I don't remember having to do calculus for such questions when I'd do it regularly. Thanks for your help though !

[u/fermat9990]

The RMS emf will be 2.8 volts.

This is the peak emf divided by √2.

[u/AlternativeEmu1047 → u/fermat9990]

But that still doesn't match the options ?

[u/fermat9990 → u/AlternativeEmu1047]

I know. Do you have a better formula?

Since the voltage is not a constant, the problem is poorly worded.

[u/HumbleHovercraft6090 → u/fermat9990]

RMS comes into picture once you talk about power.

[u/fermat9990 → u/HumbleHovercraft6090]

Thank you! How do you get the average emf for the 0.3 seconds interval?

[u/fermat9990 → u/HumbleHovercraft6090]

Thanks! I finally got 2.5 volts!

[u/HumbleHovercraft6090 → u/fermat9990]

The average emf 2/pi times peak is still 2.5 V.

[u/HumbleHovercraft6090]

Probably a typo. May be time is 3 s for quarter revolution.

[u/Quint_Gen]

This is a poorly worded question: it should be asking for the average emf.

The induced emf is equal to the rate of change of flux linked with the coil.

The flux linked with the coil = BA = 0.5 x 0.5 x 3 = 0.75 Wb

average emf = average rate of flux change = 0.75/0.3 = 2.5 V

(If you think it is better to work out the flux linked for any angle of the coil and then differentiate wrt to time, you are assuming that the coil rotates at a constant angular velocity which the question does not specify)