Solenoid & Lenz's Law: Choosing Option B

[jinhuit95]

I know that the answer will not be a or c due to effects of gravity. But I can't decide between b and d. I chose b because of lenzs law.
I thought that since the south pole enter first, there will be an increasing flux upwards, coil opposes this by inducing an magnetic flux downwards. When it leaves, the north pole will cause and decreasing flux downwards, coil will then oppose this by inducing a magnetic flux downwards. Since both induced magnetic flux are downwards, the direction of induced emf will be the same. Am I correct??

 

[PeterO]

View attachment 56680
I know that the answer will not be a or c due to effects of gravity. But I can't decide between b and d. I chose b because of lenzs law.
I thought that since the south pole enter first, there will be an increasing flux upwards, coil opposes this by inducing an magnetic flux downwards. When it leaves, the north pole will cause and decreasing flux downwards, coil will then oppose this by inducing a magnetic flux downwards. Since both induced magnetic flux are downwards, the direction of induced emf will be the same. Am I correct??

Close but no cigar.

The South pole has upward flux [ie into magnet] - as you say - and the North pole also has upward flux [ie out of magnet] .

That means the current produced as the magnet falls out of the loop is in the opposite direction to the current as it falls in.

So now you have to work out which of the two options is correct.

 

[jinhuit95]

Why are the direction of the currents different??

 

[PeterO]

Why are the direction of the currents different??

Your arguments were good except that the North pole leaving means a decreasing upward flux.

Upward, because the flux from the North end is upward, decreasing because the magnet is coming out of the solenoid.

 

[jinhuit95]

With respect to the north pole there will be an induced upwards flux right by lenzs law right? Since both induced flux are in the same direction, wouldn't the currents be in the same direction??

 

[PeterO]

With respect to the north pole there will be an induced upwards flux right by lenzs law right? Since both induced flux are in the same direction, wouldn't the currents be in the same direction??

NO.

The real flux is in the same direction. Draw a vertical Bar magnet with the South Pole at the bottom.
The flux goes into the South Pole [ie up.]
The flux comes out of the North Pole [again up]

So the real fields are in the same direction - so it all comes down to motion.

The South pole approaches the solenoid, so at that time the imposed flux density is increasing - inducing a certain current.
Later, the North pole is leaving the solenoid, so at that time the imposed flux density is reducing - inducing a current in the opposite direction.

 

[PeterO]

With respect to the north pole there will be an induced upwards flux right by lenzs law right? Since both induced flux are in the same direction, wouldn't the currents be in the same direction??

It is 2:22 am here - I am off to bed.

 

[PeterO]

With respect to the north pole there will be an induced upwards flux right by lenzs law right? Since both induced flux are in the same direction, wouldn't the currents be in the same direction??

Yes there will be an induced upward flux while the North pole is leaving, but there will be an induced downward flux when the South pole approaches.
That is why it is opposite.
The South Pole imposes an upward flux, so a downward flux is induced.
The North Pole takes away an upward flux, so an upward flux is induced.