How would an induced emf graph look like if magnetic flux varies in a sine curve?

Would it be a cosine or minus-cosine curve?

I asked this because in my book, it shows that emf just varies by being 90 degrees out of phase. So this would suggest the induced emf would just be a cosine curve as emf varies accordingly.

but in a mark scheme it says, ''According to Lenz’s law, a positive rate of change of flux (gradient) will produce a negative emf. Technically, your graph should be a -(cosine) curve''

:confused:

Reply 1

rub em out

7

I can confirm it is minus cosine, I didn't realise either until I had to sketch it in a past paper and got it wrong!

Reply 2

rub em out

7

Here, I just took a picture from my textbook which might help! As it says, emf = -gradient of flux linkage graph!

Reply 3

fuzzybear

OP

12

Original post by rub em out

Here, I just took a picture from my textbook which might help! As it says, emf = -gradient of flux linkage graph!

On your picture, the flux linkage graph shows a cosine graph, and the induced emf is shown as a sine graph

whereas the minus cosine?

Reply 4

Antimony

The induced emf graph is the negative of the gradient of the flux graph. So if it's a sine graph which starts at 0, the gradient is max positive so the emf graph starts off at max negative, when the flux reaches max, the gradient is 0 and so no emf will be induced. This makes a minus cosine graph

Reply 5

fuzzybear

OP

12

Original post by Antimony

The induced emf graph is the negative of the gradient of the flux graph. So if it's a sine graph which starts at 0, the gradient is max positive so the emf graph starts off at max negative, when the flux reaches max, the gradient is 0 and so no emf will be induced. This makes a minus cosine graph

You're talking about the gradient being max negative, right?

anyway I still don't get why emf would be a minus cosine graph, surely its just going to be an ordinary cosine graph, as the only difference is that the emf graph is shifted 90 degrees relative to the flux linkage graph. The diagram in the book shown in the 3rd post of this thread shows this (except they have it the other way round, where the flux linkage graph is a cosine and the emf graph is a sine, but still its the same = 90 degrees difference).

Reply 6

rub em out

7

Original post by fuzzybear

You're talking about the gradient being max negative, right?

anyway I still don't get why emf would be a minus cosine graph, surely its just going to be an ordinary cosine graph, as the only difference is that the emf graph is shifted 90 degrees relative to the flux linkage graph. The diagram in the book shown in the 3rd post of this thread shows this (except they have it the other way round, where the flux linkage graph is a cosine and the emf graph is a sine, but still its the same = 90 degrees difference).

You've said if the flux varies as a sine curve what will the emf vary as..
well seeing how the emf is the negative of the gradient of the flux graph, the gradient of a sin graph gives a cos shape as you should know so the negative of this makes it a -cos graph.

The difference in the example from my book is that flux is varying as a cosine graph so the gradient of a cosine graph is a minus sine graph. The negative of this gradient gives the emf so emf varies as a sine graph.

The same thing is happening in both examples except in your one the flux starts at zero giving a sine graph and in my one the flux starts at maximum flux giving a cos graph :smile:

Reply 7

fuzzybear

OP

12

Original post by rub em out

You've said if the flux varies as a sine curve what will the emf vary as..
well seeing how the emf is the negative of the gradient of the flux graph, the gradient of a sin graph gives a cos shape as you should know so the negative of this makes it a -cos graph.

The difference in the example from my book is that flux is varying as a cosine graph so the gradient of a cosine graph is a minus sine graph. The negative of this gradient gives the emf so emf varies as a sine graph.

The same thing is happening in both examples except in your one the flux starts at zero giving a sine graph and in my one the flux starts at maximum flux giving a cos graph :smile:

Ok, so basically the graph of the emf is just shifted pi/2 (90 degrees) relative to the flux graph, right?

so if the flux graph is a cosine, the emf graph is a sine.

btw, is there any reason why emf is the minus of the gradient of flux graph, and not just the gradient?

and if you look at the formula for induced emf, there isn't a minus sign :confused:

(edited 11 years ago)

Reply 8

Antimony

Original post by fuzzybear

Ok, so basically the graph of the emf is just shifted pi/2 (90 degrees) relative to the flux graph, right?

so if the flux graph is a cosine, the emf graph is a sine.

btw, is there any reason why emf is the minus of the gradient of flux graph, and not just the gradient?

and if you look at the formula for induced emf, there isn't a minus sign :confused:

There is a minus sign in the induced emf formula due to Lenz's law : E = - Nd(Φ)/dt

Reply 9

kamil999

For the question about the cyclotron, where they ask you about the magnetic field, the field in the book on page 114 is directed into the plane, and the proton moves clockwise..

Also (http://physicstasks.eu/uloha.php?uloha=551)

Reply 10

amrxo

1

Original post by fuzzybear