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

In summary, the conversation discusses how to calculate the magnetic field inside a toroidal sample of magnetic material with coils of wire carrying a current. The main question is how to express the magnetic field in terms of the relative permeability, with suggestions of using Ampere's law and finding H first before solving for B. The form of Ampere's law needed for this problem is also mentioned, along with the notation for µ.
  • #1
Nylex
552
2
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?
 
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  • #2
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.
 
  • #3
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)
 
  • #4
dextercioby said:
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.

vincentchan said:
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.
 
  • #5
The form of Ampére's law which u'll need is
[tex] \oint_{C} \vec{B}\cdot d\vec{l} =\mu_{0} I[/tex]

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

Daniel.
 
  • #6
dextercioby said:
The form of Ampére's law which u'll need is
[tex] \oint_{C} \vec{B}\cdot d\vec{l} =\mu_{0} I[/tex]

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 [tex] \oint_{C} \vec{B}\cdot d\vec{l} =\mu_{0} IN[/tex] for N coils. That wasn't the problem, it was expressing in terms of the relative permeability, which I'm still stuck on.

Thanks.
 
  • #7
How about
[tex] \oint_{C} \vec{H}\cdot d\vec{l} = IN[/tex]
and [tex]\vec{H}=\vec{B}/\mu [/tex]
 
  • #8
vincentchan said:
How about
[tex] \oint_{C} \vec{H}\cdot d\vec{l} = IN[/tex]
and [tex]\vec{H}=\vec{B}/\mu [/tex]

Which mu is that? Just [tex]\mu = \mu_{0} \mu_{r}[/tex]?
 
Last edited:
  • #9
yes... [tex]\mu = \mu_{0} \mu_{r}[/tex]
That is the standard notaion... I used to write [itex] \mu [/itex] instead of [itex] \mu_{0} \mu_{r}[/itex]
 
  • #10
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.
 

What is Ampere's law and what does it state?

Ampere's law is a fundamental law in electromagnetism that relates the magnetic field around a closed loop to the electric current passing through the loop. It states that the line integral of the magnetic field along a closed loop is equal to the permeability of free space times the total current passing through the loop.

What is the equation for Ampere's law?

The equation for Ampere's law is ∮CB•dl = μ0Ienc, where ∮CB•dl is the line integral of the magnetic field B along a closed loop C, μ0 is the permeability of free space, and Ienc is the total current passing through the loop C.

How is Ampere's law used in practical applications?

Ampere's law is used in various practical applications, such as in the design of electrical motors and generators, in the calculation of magnetic fields produced by current-carrying wires, and in the analysis of electromagnetic waves. It is also a key principle in the study of electromagnetism and is used to derive other important laws, such as Faraday's law of induction.

What is the difference between Ampere's law and Gauss's law?

Ampere's law and Gauss's law are both fundamental laws in electromagnetism, but they apply to different types of fields. Ampere's law relates the magnetic field to the electric current, while Gauss's law relates the electric field to the distribution of electric charges. Additionally, Ampere's law is valid for steady currents, while Gauss's law applies to both steady and non-steady situations.

Can Ampere's law be used to calculate the magnetic field of a straight current-carrying wire?

Yes, Ampere's law can be used to calculate the magnetic field of a straight current-carrying wire. By using a closed loop that encircles the wire, the line integral of the magnetic field can be calculated and equated to μ0I, where I is the current passing through the wire. This allows for the determination of the magnetic field at a specific distance from the wire.

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