Are My Faraday's Law Homework Solutions Correct?

[jegues]

Homework Statement

See the figures attached for each of the individual problem statements.

Homework Equations

The Attempt at a Solution

I'll start by explaining my concerns for each problem,

P1) Did I plot the Iinduced waveform correctly? I'm having some trouble picturing what the waveform of the magnetic flux would be, it seems to me as the current would increase as the flux increases so it should follow from the current waveform somewhat, correct?

P2) Is my expression for Vemf(t) correct? Is the expression I wrote down for the average power delivered to the load resistor correct?

P3) Again, I'm not sure if I've done this problem correctly, can someone check my results?

Thanks again!

 

[technician]

The falling magnet means that the loop experiences a changing magnetic flux so an emf will be induced which will give rise to an induced current in the loop.
The induced emf (and current) will oppose the change producing it (Lenz's law) which means that as the N pole approaches the loop the current will be in a direction to create a N pole (that is a current direction opposite to the direction you have drawn)
As the N pole leaves the loop the induced emf and current will change direction to produce an S pole of the loop
As the S pole approaches the loop the induced current will again oppose the change which will produce a S pole again from the loop... same current direction.
As the S pole leaves the loop the induced emf and current will be in a direction to create a N pole from the loop.
I think the curve should be 2 'pulses' going +ve...-ve...-ve...+ve

 

[jegues]

The falling magnet means that the loop experiences a changing magnetic flux so an emf will be induced which will give rise to an induced current in the loop.
The induced emf (and current) will oppose the change producing it (Lenz's law) which means that as the N pole approaches the loop the current will be in a direction to create a N pole (that is a current direction opposite to the direction you have drawn)
As the N pole leaves the loop the induced emf and current will change direction to produce an S pole of the loop
As the S pole approaches the loop the induced current will again oppose the change which will produce a S pole again from the loop... same current direction.
As the S pole leaves the loop the induced emf and current will be in a direction to create a N pole from the loop.
I think the curve should be 2 'pulses' going +ve...-ve...-ve...+ve

So basically I've mixed the direction of the currents up as the magnet passes through the loop?

 

[jegues]

Bump, still looking for verification on the other questions.

 

[DeeNos]

Hello, it's great to see you taking the time to think critically about your work and ask for feedback. Here are my thoughts on your concerns for each problem:

P1) The waveform of the induced current will follow the waveform of the magnetic flux, but it will be shifted by 90 degrees. This is because the induced current is perpendicular to the changing magnetic field. So, your current waveform looks correct, but it should be shifted by 90 degrees compared to the magnetic flux waveform.

P2) Your expression for Vemf(t) looks correct. As for the average power delivered to the load resistor, you have correctly calculated the peak value of the voltage across the resistor, but the average power should be calculated using the RMS value of the voltage. The RMS value is equal to the peak value divided by the square root of 2.

P3) Your results for this problem look correct. Just make sure to label your units for the resistance and inductance values.

Keep up the good work and don't be afraid to ask for help when needed. Science is all about collaboration and learning from each other's perspectives. Good luck with your studies!