Finding induced current (Lenz's Law)

[joej24]

Homework Statement

Attached below

Homework Equations

Emf = - [itex]\Delta[/itex][itex]\Phi[/itex] / [itex]\Delta[/itex]t
emf = vBl; motional emf

The Attempt at a Solution

In the two attached files, there are problems that ask for the direction of the induced current.
I understand that the induced current flows in the direction that opposes the magnetic flux that created it.

In the first file, [itex]\Delta[/itex][itex]\Phi[/itex] is negative because flux (BAcos[itex]\theta[/itex]) was smaller in the 2nd case than in the 1st. cos 0 > cos 60.

The opposite direction of the induced current is up because [itex]\Delta[/itex][itex]\Phi[/itex] is negative

But, how would I find out the direction of the current?

F_B = I l B sin[itex]\theta[/itex]
We only know that we need magnetic flux and magnetic field to point upwards. Without the direction of F_B, how can I use the right hand rule to find the direction of the induced current?

I have the same problem with the problem shown in the second file.
emf = vB l (memorized equation)
We then need magnetic flux out of the page and the magnetic field to do so as well.

Also, is motional emf the same as induced emf?

 

[Pi-Bond]

Do you know the right hand thumb rule? It only requires the current direction to tell you the direction of the induced magnetic field.

 

[joej24]

I guess I don't. I tried using F = I L B sin theta, but it didn't work out well.

There is another right hand rule mentioned in my book:

"The magnetic field 'lines' are actually circles whose centers are on the wire. The direction of these circles is determined by a variation of the right-hand rule. Imagine grabbing the wire in your right hand with your thumb pointing in the direction of the current. Then the direction in which your fingers curl around the wire gives the direction of the magnetic field lines."

Is this it? The magnetic field in both cases are lines, not circles.

This works for the second problem because by curling my fingers towards "out of the page", where the magnetic field should point according to Len'z law, my thumb points counterclockwise.

In the first problem when I curl my fingers upwards, my thumb points clockwise when the answer sheet says that current should flow counterclockwise.

 

[cupid.callin]

right hand thumb rule works in all cases but you just have to transform it a little

in this case : if the thumb gives the direction of mag. field then the curling fingers will give the direction of circular (or closed loop) current.

so here net flux through loop is _____ then, acc. to lenz's law, the current will be ____.

 

[Pi-Bond]

Yes, the rule your book mentions is the right hand thumb rule. The magnetic field direction you are to consider is the direction of the enclosed field (as induction is due to change in flux - which is enclosed by your loops) So in the first question your know the magnetic field is going up from the loop - if you apply the thumb rule correctly, you should agree with the answer sheet.

 

[cupid.callin]

for motional EMF you can use the eqn of force on charge in mag. field: [tex]\vec{F} \ = \ q\\vec{v}X\vec{B}[/tex]

check where wil a positively charged particle in wire will move ... that will be direction of wire ... and thus you can also find polarity of the wire.

EDIT: why isn't this LaTeX working?

 

[joej24]

Okay. For first problem, thumb represents the direction of the magnetic field (pointing up). The fingers curl counter clockwise.

For the second problem with the bars, thumb again represents the magnetic field (pointing up). And again, the fingers curl counterclockwise, which represents the direction of the induced current.

Would the right hand rule still work if we made the thumb represent the direction of the current and the fingers represent the direction of the field?

Also, what's the difference between motional emf and induced emf? When do we use each of the formulas?

 

[Pi-Bond]

The thumb is supposed to represent the current in the conventional case, I'm not sure if representing the magnetic field with the thumb will work in all cases. Using the fingers for the magnetic field lines makes more sense to me since the lines are always closed. But whatever works for you...

 

[joej24]

The thumb is supposed to represent the current in the conventional case, I'm not sure if representing the magnetic field with the thumb will work in all cases. Using the fingers for the magnetic field lines makes more sense to me since the lines are always closed. But whatever works for you...

For the first problem, the fingers would point upwards if they represent the magnetic field. The thumb could point either clockwise or counter clockwise depending on whether the palm faces towards or away from you. I don't understand how this "conventional" way is supposed to work.

 

[cupid.callin]

this is not how you use lenz law.
remember emf depends on flux not just directly in B
flux through loop in 2nd cases is (less or more?) than in 1st case.
the current now will oppose the flux change stated in last line.

so find the direction of B created by current in coil ...

and conventional method is to use thumb as B and fingers as closed current ...

 

[Pi-Bond]

No, I think the conventional rule is to use the thumb to point the current; I haven't seen the other convention in any book ever.

There should be no ambiguity here; you can apply it from any direction and the direction of current will always be the same - counterclockwise for the question you ask. The direction your fingers curl in is the direction of the magnetic field. This should take the question of the palm out here.

 

[cupid.callin]

to find direction of mag field due to current ... take thumb as current
to find direction of current due to mag field current ... take thumb as mag field

so maybe its like take thumb as whatever is given to you ...

 

[Pi-Bond]

It works here, so it's ok. I'm just saying that I haven't seen this convention elsewhere.

 

[cupid.callin]

its not really written in every book
but i saw it in a famous Physics teacher's Lecture video.
I even experimented it with over 50 questions and it proved to be true, fast and simple
Thats why i wrote it here.

 

[Pi-Bond]

Fair enough, I find the other way better because the closed fingers resemble the closed magnetic field lines more.