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The link below gives the question I'm interested in. The question is p6.2.

http://www.tkk.fi/Yksikot/Sahkomagnetiikka/kurssit/S-96.1101/harjoitukset/S961101_2006_h07.pdf

My Thoughts

OK, now I thought I knew how to do this question. The expression for the magnetic field shows that it varies with the position along y and varies with time.

So what I thought you'd do is this:

[tex]\Phi = \int{B.ds}[/tex]

Where the differential area is given as:

[tex]dS_z=dx dy[/tex]

So the above integral becomes:

[tex]\Phi = b B_0 \int{B.dy}[/tex]

where b is dx (0.1) and [tex]B_0=3 \mu T[/tex] and B is the rest of the expression for the varying magnetic field.

So I thought you'd integrate this expression with limits of 0 to 0.3, but the answer I get is nothing like their answer??

I end up with an expression for the currentiof:

[tex]i=- \frac {B_0 b \omega} {R k}[ cos(\omega t -k a)-cos(\omega t)][/tex]

This is nothing like their expression of:

[tex]i=- \frac {B_0 b \omega} {R k} [sin(\frac {1} {2} k a) sin(\omega t- \frac {1} {2} k a)][/tex]

This is simplified by them in the hints section (just scroll down the page to find the hints).

So what am I doing wrong here??

EDIT: oops my expressions for I are meant to contain cosines and not sines.

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# Homework Help: Time-Varying Magnetic Field

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