Simple toriodal solenoid formulae and values

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Created this as a copy of Simple toriodal solenoid question.

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Question statement

A torus made of a material with a relative permeability of {mur} has a wire wound around it {turns} times. The torus has circular cross section of area {areacm} cm $^2$ and the ring has an overall radius of {radius} cm. This solenoid is then connected to a power supply, and a current of {current} Amps is passed through the wire.

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

area	number	0.0004523893
areacm	number	4.524
bfield	number	2.2934117647
current	number	0.8
energy1	number	0.7491
energy2	number	3.0
hfield	number	13518.8081073351
inductance	number	2.3408933077
mmf	number	1444
mu0	number	0.0000012566
mur	integer	135
newcurrent	number	1.601
newturns	number	3612
pathlength	number	0.1068141502
phi	number	0.001037515
psi	number	1.8727146462
radius	number	1.7
rcore	number	0.012
rring	number	0.017
turns	integer	1805
newperm	number	0.0006794
newmur	number	540.6493416832

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
pi rcore^2

JME function reference

Description

cross-sectional area of core in m^2.

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`

0.0004523893

← Depends on:

rcore

→ Used by:

areacm
newcurrent
newperm
newturns
phi

Parts

Magnetomotive force Gap-fill
1. Gap mmf Number entry
  Add
Magnetising field strength Gap-fill
1. Gap H Number entry
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Magnetic flux density Gap-fill
1. Gap B Number entry
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Magnetic flux in the core Gap-fill
1. Gap phi Number entry
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Flux linking the coil Gap-fill
1. Gap phi Number entry
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Inductance Gap-fill
1. Gap L Number entry
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Information only
Redesign option 1 Gap-fill
1. Gap Turns Number entry
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Redesign option 2 Gap-fill
1. Gap Current Number entry
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Redesign option 3 Gap-fill
1. Gap Permeability Number entry
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2. Gap Relative permeability Number entry
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Gap-fill

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

Calculate the magnetomotive force (MMF).

MMF $=$ mmf 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

$\text{Stored energy}={1\over2}Li^2=$ {energy1} Joules

In the redesign questions, it's simplest to write out the full equation dependence of the quantity being sought upon the variable being changed.

For the energy dependence upon the number of turns, we can write

$\displaystyle \text{Stored energy}={1\over2}Li^2={1\over 2}{\Psi\over i}i^2={1\over 2}{N\phi}i={1\over 2}NBAi={1\over 2}N\mu HAi={1\over 2}N\mu {Ni\over 2\pi R}Ai={\mu Ai^2 \over 4\pi R}N^2$

Thus, the energy stored is proportional to the number of turns squared, so, say, to increase the stored energy by a factor of 4 one would need to double the number of turns. This may not be feasible as there may be space constraints, and an increased number of turns will increase the electrical resistance of the coil.

Give a worked solution to the whole question.

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This question is used in the following exams:

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.
Magnetism test by Jon Goss in ENG1003 20-21.

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Simple toriodal solenoid formulae and values

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Simple toriodal solenoid formulae and values

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, 2 months ago

Jon Goss 5 years, 2 months ago

Error in variable testing condition

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