What is Magnetic energy: Definition and 50 Discussions
Magnetic energy and electrostatic potential energy are related by Maxwell's equations. The potential energy of a magnet or magnetic moment
m
{\displaystyle \mathbf {m} }
in a magnetic field
B
{\displaystyle \mathbf {B} }
is defined as the mechanical work of the magnetic force (actually magnetic torque) on the re-alignment of the vector of the magnetic dipole moment and is equal to:
E
p
,
m
=
−
m
⋅
B
{\displaystyle E_{\rm {p,m}}=-\mathbf {m} \cdot \mathbf {B} }
while the energy stored in an inductor (of inductance
L
{\displaystyle L}
) when a current
I
{\displaystyle I}
flows through it is given by:
E
p
,
m
=
1
2
L
I
2
.
{\displaystyle E_{\rm {p,m}}={\frac {1}{2}}LI^{2}.}
This second expression forms the basis for superconducting magnetic energy storage.
Energy is also stored in a magnetic field. The energy per unit volume in a region of space of permeability
μ
0
{\displaystyle \mu _{0}}
containing magnetic field
B
{\displaystyle \mathbf {B} }
is:
u
=
1
2
B
2
μ
0
{\displaystyle u={\frac {1}{2}}{\frac {B^{2}}{\mu _{0}}}}
More generally, if we assume that the medium is paramagnetic or diamagnetic so that a linear constitutive equation exists that relates
B
{\displaystyle \mathbf {B} }
and
H
{\displaystyle \mathbf {H} }
, then it can be shown that the magnetic field stores an energy of
E
=
1
2
∫
H
⋅
B
d
V
{\displaystyle E={\frac {1}{2}}\int \mathbf {H} \cdot \mathbf {B} \ \mathrm {d} V}
where the integral is evaluated over the entire region where the magnetic field exists.For a magnetostatic system of currents in free space, the stored energy can be found by imagining the process of linearly turning on the currents and their generated magnetic field, arriving at a total energy of:
{\displaystyle \mathbf {J} }
is the current density field and
A
{\displaystyle \mathbf {A} }
is the magnetic vector potential. This is analogous to the electrostatic energy expression
1
2
∫
ρ
ϕ
d
V
{\textstyle {\frac {1}{2}}\int \rho \phi \ \mathrm {d} V}
; note that neither of these static expressions do apply in the case of time-varying charge or current distributions.
For ##a<r<b## we can calculate the magnetic field at some radius ##r## with Ampere's law
$$\oint_C\vec{B}\cdot d\vec{l}=\mu_0 I_{enc}=\mu_0 I$$
$$\implies B=\frac{\mu_0 I}{2\pi r}$$
$$\vec{B}=\frac{\mu_0 I}{2\pi r}\hat{\theta}$$
At this point my questions arise.
I don't see a current loop...
Can a train (e.g. like a maglev train) use a set of permanent magnets (not electromagnets) that somehow can be propelled and maintain at least a constant speed with them?
Is this an example of such system...
Hi,
The problem I am working on requires me to work out the the pressure on the outer conductor of a coaxial cable due to the current on the inner one.
This cable carries a dc current of 5000 Amps on the inner wire of radius 2 cm. The outer cylindrical wire of radius 5cm carries the return...
How would you go about calculating the work done in morphing a square current-carrying loop into a circular current-carrying loop, without change in length while maintaining the same angular orientation with an external magnetic field.
My book suggests defining P(potential energy) = M.B (dot...
The current density between the plates is J = 1 A/m2. So, I have to calculate first the magnetic energy in the whole space. Out of the sheets, there is no current, so the magnetic energy would be 0 in that places. Hence,
U = J(1/2) \int_{inside the plates}A(r)dr, where A(r) is the vector...
Hi,
I have to find the magnetic energy inside a coaxial cable of inner radius ##a## and outer radium ##b##, ##I = I##
By using Ampere's law
if ##r<a##
##B = \frac{\mu_0Ir}{2\pi a^2}##
if ##a<r<b##
##B = \frac{\mu_0I}{2\pi r}##
if ##r>b##
##B = 0##
Then, the energy in a magnetic field ##E_b...
The magnetic energy of a current carrying spring, with ##N## turns, length ##x## and cross sectional area ##A##, is $$E_m = \frac{\mu_0 N^2 I^2 A}{2x}$$The (negated) spatial derivative of this yields a quantity with dimensions of force,$$F = - \frac{dE_m}{dx} = \frac{\mu_0 N^2 I^2 A}{2x^2}$$How...
I first calculated Magnetic field at a distance x using Ampere's law.Then i took an element and wrote its inductance using L=Flux/Current.
Then i integrated from a to b.
But i arrived at nothing.
Help.
I cam across SMES (Superconducting Magnetic Energy Storage) while researching superconducting and had a few questions I'm hoping to have answered.
1. I have read that SMES devices are primary used in the event for short interruptions in power, and aiding in efficiency in the power grid. Can a...
Homework Statement
So I came across with following problem:
> Consider a cylindrical conductor of infinite length and circular section of radius a and that is traversed by a stationary current I. What is the magnetic energy stored in the conductor.
Homework Equations
3. The Attempt at a...
A long thin current-carrying conductor have a magnetic field around it in the direction according the RHR. If a compass needle was placed beside the wire it moves to point in the direction of the magnetic field. Now the current in the wire doesn't diminish and can still light a bulb in its way...
Hi - On this forum, dgreenheck on May 20, 2013 touched on this area. I will post my question in this manner:
Say one has a solenoid with a given number of turns; if the core is air, we know that if we run 10 amps through the circuit, the energy to charge a magnetic field to "B" Tesla is...
Hello
Before I start, I would like to clarify that I know Perpetual Motion is not possible & Energy can neither be created nor destroyed, But Can be change from one form to another.
That's exactly my point. If I could convert energy from one to another, then why couldn't I just harness energy...
As we know, work done by an outside agency in creating some current ''I" in an inductor 'L' is 1/2LI2. Now this result is derived by quasistatic approximation if I am not wrong. Now, I am assuming that in non quasistatic (real) scenarios, the work done by outside agency would be different(If you...
Hi,
I have a problem with the fomular
u=m·B
and
u=B^2/4pi
Since I want to calculate how many magnetic energy on a solenoid, I couldn't decide which fomular should I use.
Homework Statement
A cylindrical conductor of radius ##a## has a hole of radius ##b## and there is a current ##i## uniformly spread inside the conductor.
Calculate the magnetic energy of the conductor.
Homework Equations
$$U_{m}=\int_{Volume} \frac{B^2}{2 \mu_0} dV$$
The Attempt at a...
How large would a superconducting magnetic energy storage device be if it were to safely carry 100 kilowatt-hours of energy? How much cryogen (liquid nitrogen) would it consume per hour if the device were made from high-temperature superconducting materials (YBCO or similar).
Homework Statement
In an atom: suppose one electron orbits the n proton nucleus at radius r . Find the magnetic energy density, in J/m3, at the center of the atom due to the motion of this electron.
NOTE: You can ignore the effect of other electrons in this atom.
Homework Equations...
Storing energy in a system means to raise the internal energy of it. A system could be in superconducting phase because the latter has correspondingly lower internal energy. How can energy be stored in a phase that has the lower energy? When energy is injected into the system, it would leave...
is seems to be generally agreed upon that any "magnet" comes into being because it has been infused by an Electric Current.
so, my question:
so this magnetic energy is imparted to the material by the electric current.
so, then, what is "magnetic energy" ? are there "Magnetons"?
Hi, I would appreciate some help here as its been some 25 years since leaving school and I am now expected as part of my duties and training for a youth leader in a cub scout pack to provice some activities in relation to Beaver Cubs and activity badges.
Subject... Magnets.
Now I...
Consider a situation where you have a charge at rest in a uniform magnetic field.A sharp impulse is given to the charge in a direction perpendicular to the magnetic field,if the velocity is high enough the charge which starts revolving in circular path should behave like a current carrying...
I have a question about solenoids.
The formula for the magnetic field energy density is:
\frac{1}{2}\frac{B^{2}}{μ}
If I have an air-filled core, then μ=μ0. If I have a steel core, then μ will be ~ 100μ0. This implies that an air-filled core solenoid stores more energy than a steel core...
Hi guys! I was wondering something about magnetic energy and well, I stumbled on to this. If there was a way to use a magnetic field's energy without influencing the actual magnet, would the degradation of the field increase at a faster rate?
Can anyone give me some feedback on my understanding of this proposed experiment?
The device consists of 2 wound solenoids, each forming a closed loop.
One solenoid is slightly smaller as to be able to fit inside of the outer solenoid.
The smaller solenoid is accelerated by compressed air...
Homework Statement
What are the units for electric energy density and magnetic energy density? Is it J/m^3
Homework Equations
μ(mag)= (B2)/ (2μo)
μ(electric) = (1/2) (εo) (E2)
The Attempt at a Solution
Magnetic energy density : T2/ N/A2 = J/m^3
electric energy density...
Cheers everybody,
I've got a question about an equation in the famous paper "The Effect Of Retardation On The Interaction Of Two Electrons" by G. Breit. There on the first page, it is said, that a first guess for a two electron relativistic wave equation is made by constructing the...
Hello. So: Why does magnetic force tend to increase magnetic energy?
1) Usually, forces go in the direction of energy minimums. Why in this case is the opposite?
2) What does it imply?
What is that makes magnetism particular in some senses, for example this, for example its force function...
Hello
I am new in this forum and also my knowledge on physics is not very good.
Now i am trying to understand how the permanent magnets work. We know that if we take ferromagnetic materials and by doing a specific process we can create a magnet. Then by subjecting the magnet into a high...
Homework Statement
In the above circuit, the EMF from the battery is 12 V and the resistor has a resistance is 6.6 Ω. The inductor consists of a long, thin cylindrical coil of wire with 30000 turns, a radius of 5 cm and a length of 61 cm.
Answer the following questions for a time 1.4...
Homework Statement
In a circuit composed of a battery a resistor and an inductor, the EMF from the battery is 12 V and the resistor has a resistance is 7.4 Ω. The inductor consists of a long, thin cylindrical coil of wire with 20000 turns, a radius of 5 cm and a length of 61 cm.
Answer...
Homework Statement
A long straight wire of radius r=a carries a current I uniformly distributed over its cross section. Show that the magnetic energy per unit length (energy density u=B^2/2mu) is given by \mi_{o}\ =\ 4\pi\ \timesI^2\ 10^{-7}/16pi. What is the contribution that a single long...
Inspired by this thread https://www.physicsforums.com/showthread.php?t=451674, I had an idea!
And it is just that: an idea. Can anyone tell me if it would work, in theory? And if not, why not?
So, passing a magnet through a coil of wire produces an electric current. But it will always...
Ok, so I've been thinking about this for a while now, but seeing as I am still in high school i really do not have much of a background to help me out with this. My dad asked me a while ago if we had ever discussed perpetual motion machines, and of course that got me thinking on how one could...
I was reading an article, and it said that the total free energy of the system in an external magnetic field H can be written as:
F= 0.5 * χe^(-1) * Me^2 + 0.5 * χl^(-1) * Ml^2 - Jeff*Ml*Me - (Ml+Me)H
Where Ml and Me denote the magnetization for the local moment and electron subsystem. J_eff...
Homework Statement
Considering the Earth magnetic field, I need to find the magnetic energy stored in our classroom.Homework Equations
U= (1/2*\mu) B2
The Attempt at a Solution
Any suggestions?
Can anyone point me in the direction of good information on magnet's, magnetic energy, magnetic forces. Or does anybody have a good understanding of this?
Would really like to find somewhere that I can order magnets. Or better yet, make good one's myself, or find out how to find rare Earth...
1. My teacher has given me a poster board to do on magnetic energy even though she has explained nothing about the subject, nor is there anything in my book. I am looking for the formula for finding magnetic energy and examples from everyday life.
All I got was 1/2BH, but I have no idea what...
Homework Statement
A small circular loop, radius a in the xy plane, carries current I which creates a magnetic moment pointing in the z direction. A magnetic induction field B= (s/y^3)z is applied to the loop where s is a constant, y is the distance in the plane of the loop from an arbitrary...
[SOLVED] Magnetic Energy
Whoops, never mind, i didn't use the right B field
Homework Statement
Show that the magnetic energy per unit length of a nonmagnetic wire is \frac{\mu_0 I^2 }{ 16 \pi} (inside the wire)
Homework Equations
W = 1/2 L I^2
W = \int \int \int \frac{|B|^2}...
Homework Statement
How can be shown that the electric energy density is completely dominated by the magnetic energy density for non-relativistic plasmas?
Homework Equations
the electric energy density is given by {\epsilon_{0}.E^{2}}{}, and the magnetic energy density is given by...
Hi everyone,
this is a hard question (at least for me):
For a coaxial cable (description see below) find the magnetic energy stored in a cylindrical annulus of unit length, raduius r and thickness dr, in the regions 0<r<a and a<r<b.
Hence by integration find the magnetic energy stored...
I just started physics, I am in 11th grade and we needed to do a project in some class and I want to do this, but I really need help. I asked my teacher about doing something on magnetic energy (I would have no clue where to begin though…) and she brought up plasmas and doing something on those...
"Magnetic energy? Perhaps"
Okay, I had to post this one...
First I saw this
which just about had me coming out of the chair - ever heard of a generator? But it gets better.
And here's the part that will get a real reaction I'd bet:
See the entire article here...
Using magnetic energy...
I am not sure if this is the right place for this type of discussion, but I am wondering if it is possible to suspend a magnet (permanent magnet) among other permanent magnets in such a way, that it will rotate by it self based on arrangement of mantic fields as such...