Flux Question

[vamsiaus]

Hey, this is a question from the Neap 07 exam2. I am not sure if what i have done is wrong but according to the solutions I am. I dont really understand the concept behind the graphs, as in the shape and where it begins. Firstly attached is Q13 from the Neap exam.
1.  Magnetic flux is the product of the field and the area of the loop right? The answer has it one decimal off to my answer.
     change in flux = BA = .5 x .02 = .01 wb. This is my answer.
The solutions have it as .1 wb.

2. I got it Wrong as a result of question 1. But this is my process:
    Emf= change in flux / change in time = .01/.05 = .2 volts.
The answer is 2 volts with a negative. When do i put this negative, and when do i leave. Is it wrong if I don't have a negative.

3. Alright this is what I don't get at all.
        1. Do all DC graphs not go below the x-axis. Why?
        2. I got the right graph but just not sure behind the theory. Initially the coil is parallel to the magnetic field and thus according to the equation (change in flux = BA costheta) since theta = 0, the magnetic flux should be at a max to start off with. Since flux is at a max, so should EMF. I am just not sure about whether or not this theory is right though.
4. I have come across some of these questions where in the process of finding out the magnetic flux, the solutions deliberately leave out the number of turns in a coil. I was just not able to pick up the pattern on this. When do I use the 'n' in the formula(flux = nBA), and when do I leave it out.

These maybe noob questions, but due to our stupid school any explanations regarding these questions are never made in class. So lacking a bit of theory knowledge.
Thanks in advance to anyone who can help.

[Edmund]

Had similar problems with this question last year. For question 13, flux should be zero because no field lines are passing through the loop at the instant shown in the diagram.

[vamsiaus]

But there is a rotation, doesn't that mean that a force exists. For a force to exist doesn't there need to be a current flowing through the loop?

[kamil9876]

Since flux is at a max, so should EMF. I am just not sure about whether or not this theory is right though.

In fact the opposite is true. When flux is max or min the emf is 0 and when flux is 0 the emf is at it's max or min. In order to explain why I could use calculus(maths methods will suffice) but I don't know if you do the subject so I'll try not to. Say flux is at a max when . When the flux is just below maximum (where is a small duration of time). When (just before flux being maximum) the flux is also just below max. In fact if we compute the average emf between and :


Using the fact that the expression evaluates to .

Play around with the formula by computing changes in flux over littile time intervals and see how the emf varies.


As for the signs, it's all about the direction given by lenz's law. In this case the current is in one direction since every half turn the ends of the coil swap with each other and hence are touching the different part of the commutator, and this cancels out the natural change in direction that occurs every half turn in the coil(you can check this by using the and lenze's law .



Feel free to ask for clarifications.

[vamsiaus]

Say for the situation in the exam. Since the coil is in parallel with the magnetic field, the flux would be max according to the rule right? Then since Emf is a derivative function of the mag flux, shouldn't the emf start at 0 then. (The solutions have it starting with a max as in a cos graph not sin.

[kurrymuncher]

Say for the situation in the exam. Since the coil is in parallel with the magnetic field, the flux would be max according to the rule right? Then since Emf is a derivative function of the mag flux, shouldn't the emf start at 0 then. (The solutions have it starting with a max as in a cos graph not sin.

No, the flux is not maximum when the coil is parallel to the magnetic field. The cos(thetha) in the flux formula is the angle the flux makes with the normal of the coil plane. therefore, when the coil is parallel, the angle between the flux and the normal of the plane is 90 degrees, therefore flux=BAcos(90). Cos(90)=0, hence the flux is zero when the coil is parallel to the magnetic field. Remember that angle is between the flux and the normal of the coil plane.

So, as the magnetic flux is zero, when the coil begins to rotate, the flux vs time graph will look like a sine graph. To get the EMF vs time graph, you have to take the NEGATIVE derivative of the flux graph, therefore, the EMF vs time graph will be a cos wave.

[vamsiaus]

I have never heard about the normal of the plane lol. Where is the normal located exactly. if u could just draw a picture on where that'd be, it would be really nice.

[kurrymuncher]

[IMG]http://img71.imageshack.us/img71/9395/13453050.jpg[/img]

notice how the angle between the plane of the coil and the flux is 90 degrees, therefore cos (90) is zero, so the flux is zero.

sketch isn't that great, but I tried lol  :laugh:


flux= green lines

[kamil9876]

Say for the situation in the exam. Since the coil is in parallel with the magnetic field, the flux would be max according to the rule right? Then since Emf is a derivative function of the mag flux, shouldn't the emf start at 0 then. (The solutions have it starting with a max as in a cos graph not sin.

The flux would initially be zero as kurrymuncher pointed out. The emf(Voltage) will initially be as a max, in agreement with what i said earlier and the solutions (cos graph).

[vamsiaus]

aww thanks for the help guys really appreciate it. One more question, attached is q3 from Lisachem 2007 exam.

The question asks for the direction of the north pole and the compasses are showing.

This is what I thought. Since the current is travelling up the wire, using the right hand grip rule the direction of the field is clockwise(when viewed from the top). Then I thought that field always goes from North to South, so the direction of the North in that field will be in the opposite side of the direction of the field (as field is travelling from North to south, and I want North). Thus I chose C, but the answer is B. Not Sure why though.

Thanks 

[vamsiaus]

bump...

[sachinmachin]

aww thanks for the help guys really appreciate it. One more question, attached is q3 from Lisachem 2007 exam.

The question asks for the direction of the north pole and the compasses are showing.

This is what I thought. Since the current is travelling up the wire, using the right hand grip rule the direction of the field is clockwise(when viewed from the top). Then I thought that field always goes from North to South, so the direction of the North in that field will be in the opposite side of the direction of the field (as field is travelling from North to south, and I want North). Thus I chose C, but the answer is B. Not Sure why though.

Thanks 

yeh the answer would be B. im guessing you've used the right hand grip rule, but have managed to get the direction of the magnetic field wrong. because the current is travelling upwards, your thumb should point up. thus the magnetic field would be anticlockwise as you wrap your fingers around the wire which should curl around in an anticlockwise direction. dont worry, i used to do the same mistake as you, as i constantly muddled up the right hand grip rule.

[vamsiaus]

yea, i know how to use the grip rule lol. But doesn't field travel from north to south, so the direction of field would be in the direction opposite to the side shown by the compass (which points north).

[sachinmachin]

yea, i know how to use the grip rule lol. But doesn't field travel from north to south, so the direction of field would be in the direction opposite to the side shown by the compass (which points north).

remember for current carrying wires, you cannot assume the direction of magnetic field unless there are two magnets (different polarity) on either side of the wire. especially when you use the right hand grip rule, you must be careful as to how you see the direction of which your fingers curl around. i suggest maybe looking at checkpoints, and do about 20 questions of this type (other sources as well) until you feel you've got some understanding of how it works.

[vamsiaus]

So, for these sort of questions, would u just assume that the direction of the magnetic field is North and that the compass would point in the direction of the magnetic field(north).