Calculating Magnetic Field Inside a Toroidal Sample Using Ampere's Law

[Nylex]

Can someone help me with this please?

Consider a toroidal sample of magnetic material wound, uniformly, with coils of wire that carry a current I. If the total number of coils is N and the relative permeability of the material is μr, calculate the magnetic field B, inside the toroid at radius r.

The problem is expressing the magnetic field in terms of the relative permeability. In my notes, I have H = B/μ0μr, but I can't use that can I? I mean, I can't substitute B = μ0μrH into the Ampere's law integral, right?

 

[dextercioby]

Of course u can,but viceversa,because Ampère's law contains H and u'll need to contain B.

It would be really helpful if that µ_{r} would be constant,as it would come out of the integral,just like I and µ_{0}.

Daniel.

 

[vincentchan]

you don't need integral for this problem... find H first, then B
H is easy...the formulas for H in a toroidal is...(hints: if your calculation takes you more than 10 seconds, that's mean you are going to a wrong way)

 

[Nylex]

Of course u can,but viceversa,because Ampère's law contains H and u'll need to contain B.

It would be really helpful if that µ_{r} would be constant,as it would come out of the integral,just like I and µ_{0}.

Daniel.

I have only seen Ampere's law in the form of B . dl = µ0I (well, there's a form for simple media, H . dl = J . dS afaik, but I don't know what I'd use as dS :/). The µr is a constant in the question.

you don't need integral for this problem... find H first, then B
H is easy...the formulas for H in a toroidal is...(hints: if your calculation takes you more than 10 seconds, that's mean you are going to a wrong way)

I don't know what the formula for H in a toroid is! The version of Ampere's law with H (without displacement currents) and stuff is the one above.

 

[dextercioby]

The form of Ampére's law which u'll need is
$$\oint_{C} \vec{B}\cdot d\vec{l} =\mu_{0} I$$

which should give you the field created by 1 coil.For N,figure out what should b done.

Daniel.

 

[Nylex]

The form of Ampére's law which u'll need is
$$\oint_{C} \vec{B}\cdot d\vec{l} =\mu_{0} I$$

which should give you the field created by 1 coil.For N,figure out what should b done.

Daniel.

Yeah, I know you just use $$\oint_{C} \vec{B}\cdot d\vec{l} =\mu_{0} IN$$ for N coils. That wasn't the problem, it was expressing in terms of the relative permeability, which I'm still stuck on.

Thanks.

 

[vincentchan]

How about
$$\oint_{C} \vec{H}\cdot d\vec{l} = IN$$
and $$\vec{H}=\vec{B}/\mu$$

 

[Nylex]

How about
$$\oint_{C} \vec{H}\cdot d\vec{l} = IN$$
and $$\vec{H}=\vec{B}/\mu$$

Which mu is that? Just $$\mu = \mu_{0} \mu_{r}$$?

 

[vincentchan]

yes... $$\mu = \mu_{0} \mu_{r}$$
That is the standard notaion... I used to write $\mu$ instead of $\mu_{0} \mu_{r}$

 

[dextercioby]

Of course one writes always µ when it comes to magnetic fields in matter,not in vacuum.Just because µ_{0} is an universal constant and µ_{r} is an adimensional constant,it's pointless to always write the product.

Daniel.