Characteristics of a toriodal solenoid

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Question statement

A toriodal solenoid is constructed to act as an inductor. It has the following properties:

{turns} turns of wire, $N$
{rcore*100} cm core radius, $r$
{rring*100} cm ring radius, $R$
{mur} core relative permeability, $\mu_r$ (mu_r)
{current} A current in the coil, $i$

When entering formulae use only the above symbols along with the symbol for permeability of free space, $\mu_0$ (mu_0), the magnetic flux, $\phi$ (phi), the magnetic flux density, $B$ , the magnetising field strength, $H$ , the flux linkage, $\Psi$ (psi), the inductance, $L$ , the reluctance, $S$ , and the stored energy, $U$ . In each case use the simplest formula based upon the quantity from the previous part.

When providing numerical answers you may express them using scientific notation. Express values to four significant figures and use the values of physical constants as provided in the course notes.

Give any introductory information the student needs.

			Name	Type	Generated Value

Bfield	number	0.216
Bsat	number	1.416
current	number	0.9
energy	number	0.0390864392
Hfield	number	1145.9155902616
inductance	number	0.0965097263
isat	number	5.9
mmf	number	288
mu	number	0.0001884956
mu0	number	0.0000012566
mur	integer	150
phi	number	0.0002714336
psi	number	0.0868587537
rcore	number	0.02
reluctance	number	1061032.953945969
rring	number	0.04
turns	integer	320
xsection	number	0.0012566371

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
mur * mu0 * Hfield

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `number`

0.216

← Depends on:

Hfield
mu0
mur

→ Used by:

Bsat
phi

This variable doesn't seem to be used anywhere.

Parts

MMF Gap-fill
1. Gap MMF formula Mathematical expression
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2. Gap MMF value Number entry
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Magnetising field strength Gap-fill
1. Gap H formula Mathematical expression
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2. Gap H value Number entry
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Magnetic flux density Gap-fill
1. Gap B formula Mathematical expression
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2. Gap B value Number entry
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Magnetic flux Gap-fill
1. Gap $\phi$ formula Mathematical expression
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2. Gap $\phi$ value Number entry
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Flux linkage Gap-fill
1. Gap $\Psi$ formula Mathematical expression
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2. Gap $\Psi$ value Number entry
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Inductance Gap-fill
1. Gap Inductance formula Mathematical expression
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2. Gap L value Number entry
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Reluctance Gap-fill
1. Gap Reluctance formula Mathematical expression
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2. Gap S value Number entry
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Stored energy Gap-fill
1. Gap Energy formula Mathematical expression
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2. Gap Energy value Number entry
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Current for saturated field Gap-fill
1. Gap Current formula Mathematical expression
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2. Gap Current value Number entry
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Post saturation inductance Choose one from a list

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Ask the student a question, and give any hints about how they should answer this part.

The mathematical expression for the MMF is ${\rm MMF} =$ MMF formula.

The value of the MMF is MMF value Amps.

Advice

This question is an example of a series of linked quantities.

${\rm MMF}= N i=$ {mmf} Amps

$|H|=\displaystyle{{\rm MMF}\over {\rm path~length}}=\displaystyle{Ni\over2\pi R}=$ {Hfield} A/m

$|B|=\mu_0\mu_r|H|=\mu|H|=$ {Bfield} T

$\phi=B A=$ {phi} Wb

$\Psi = N \phi=$ {Psi} Wb

$L = \displaystyle{\Psi\over i}=$ {inductance} Henrys

$\text{Stored energy}={1\over2}Li^2=$ {energy} Joules

The field that a given ferro-magnetic material can amplify is limited to its saturation value. Raising the current beyond this point does not increase the flux density beyond the base-line $\mu_0$ level. If we know the saturation field, $B_{\rm sat}$ , then we can determine the current since we can re-arrange the formulae above to give

$B_{\rm sat}=\mu H=\displaystyle{\mu N i_{\rm sat}\over 2\pi R}\Rightarrow i_{\rm sat}=\displaystyle{2\pi RB_{\rm sat}\over \mu_0 \mu_r N}=$ {isat} Amps

The flux-linkage rises up to the point of saturation, so a current increase beyond this point simply reduces the inductance (since $L=\Psi_{\rm sat}/i$ ).

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This question is used in the following exams:

Tutorial sheet 2 - magnetism by Jon Goss in EEE1001 & PHY1023.
All electromag by Jon Goss in EEE1001 & PHY1023.
TEST by Jon Goss in Jon's workspace.
E&M 9: Toroidal solenoid quiz by Jon Goss in EEE1001 & PHY1023.
Digital Tutorial: Week 7 by Jon Goss in EEE1001 & PHY1023.

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Jon Goss 4 years, 1 month ago

Jon Goss 5 years, 5 months ago

Jon Goss 5 years, 5 months ago

Jon Goss 5 years, 5 months ago

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Characteristics of a toriodal solenoid

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Jon Goss 4 years, 1 month ago

Jon Goss 5 years, 5 months ago

Jon Goss 5 years, 5 months ago

Jon Goss 5 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`