Electromagnet magnetic field strength

[Sum Guy]

Homework Statement

Homework Equations

$\oint_{C} Bd\ell = \mu I_{enc}, B_{normal}$ continuous across boundary, $H_{parallel}$ continuous across boundary

The Attempt at a Solution

$$\oint_{C} Bd\ell = \mu I_{enc} \rightarrow B = \frac{\mu NI}{2\pi r}$$

Any help much appreciated. How should I proceed?

 

[mfb]

How did you do the "->" step?
Where do you run into problems with the other parts?

 

[Sum Guy]

How did you do the "->" step?
Where do you run into problems with the other parts?

I just don't know how to even get started really. I did the "->" just by applying amperes law, ignoring the ends of the core (because you could just take a line integral to avoid them).

 

[mfb]

... and ignoring the core, and assuming B is uniform in the gap. That is fine, but you should be aware of assumptions like that.

The untapered magnet works in the same way as the tapered magnet, you just have fewer variables (which makes it a bit easier).

 

[Sum Guy]

... and ignoring the core, and assuming B is uniform in the gap. That is fine, but you should be aware of assumptions like that.

The untapered magnet works in the same way as the tapered magnet, you just have fewer variables (which makes it a bit easier).

So what should I do? :S

 

[mfb]

The same thing as for the tapered magnet.

 

[Sum Guy]

The same thing as for the tapered magnet.

Please could you give me a clue as to what integral I would have to do? I'm struggling to see how I am meant to take account of the tapering in an integral amperean loop...?

 

[mfb]

It is literally exactly the same as the exercise you solved already, just with different letters because the ends are not tapered.

 

[Sum Guy]

It is literally exactly the same as the exercise you solved already, just with different letters because the ends are not tapered.

I haven't solved the tapered case? I don't know how to..?