Question

can anybody explain magnetic moment?

Answer 1

You mean magnetic dipole moments?

Answer 2

yes

Answer 3

can you be a bit more specific please? what part of the concept do you need help with?

Answer 4

i want to understand ampere's law whose statement mathematically represented as:
\[\int\limits_{}^{}B.ds = \mu i\]

Answer 5

that \(\mu_0=4\pi\times10^{-7}\) is a universal constant, like \(\epsilon_0\), and is not the at all the same as the magnetic dipole moment (which is a vector) \(\vec\mu=NIA\hat n\).
Don't let the use of the same Greek letter confuse you!

Answer 6

\[\oint\vec B\cdot d\vec s=\mu_0 I\]is how the law is stated

Answer 7

oh..thanks,but can you explain the magnetic moment also?

Answer 8

because i want to know the diffference between dipole moment & magnetic moment..if any..and i couldn't found the required symbols so apology regarding that

Answer 9

best way to describe the magnetic dipole moment it for me is to derive it.... but to me "magnetic moment" is 'magnetic dipole moment", that is to say that the magnetic moment \(\vec\mu\) is a particular kind of dipole moment, as opposed to the electrical dipole moment \(\vec p\)

Answer 10

what do you mean by opposed to electric dipole moment?

Answer 11

I mean that in electricity and magnetism we tend to talk about only two dipole moments, the electric dipole moment and the magnetic dipole moment.

Answer 12

magnet dipole moment is?

Answer 13

magnetic dipole moment is \[\vec\mu=NIA\hat n\][ where \(N\) is the number of windings of a coil, \(I\) is the current running though the coil, \(A\) is the area of each coil, and \(\hat n\) is the unit normal vector perpendicular to the area of the coil as defined by following the current with the right hand rule

Answer 14

in effect it acts like a bar magnet

Answer 15

can you explain the magnetic dipole moment due to orbital motion of electron..its expression as i know is:
\[\frac{ eL }{ 2m }\]
where L is the angular momentum ,e is the charge on electron & m is its mass.

Answer 16

never seen that before, let me see if I can derive that...

Answer 17

got it, so first what is the angular momentum of the particle?

Answer 18

its from atomic & nuclear magnetism..

Answer 19

h/2pi

Answer 20

I mean in classical terms, what is the momentum of a point moving in a circle?

Answer 21

I don't know how to derive this starting from Plank's constant, but I was able to do it classically

Answer 22

its mvr

Answer 23

good, and what is the period for the revolution of the electron?

Answer 24

2pi/w

Answer 25

w is angular velocity.

Answer 26

right, but let's keep our variable to a minimum and write w=v/r

Answer 27

variables*

Answer 28

yes i know this expression

Answer 29

variables?

Answer 30

the unknowns; the letters are called "variables" in English, m, v, r, etc. all variables

Answer 31

yes i know the definition but here how many variables we have:m,v,r,w?

Answer 32

so we have that L=mvr and T=2pi(r/v) correct?
now find the current

Answer 33

well we can relate w to r and v, so let's do that so that we don't have more different variable than we need.

Answer 34

yes but i just want to get the explanation about the result that is:
eL/2m

Answer 35

we will get there if you find the current and apply the definition of magnetic moment

Answer 36

ok let me do that:
current is:q/t
for electron it is:e/t
then?

Answer 37

yes, and what is t in our case?

Answer 38

i got
i=ev/2(pi)r
by putting time & w=v/r

Answer 39

exactly, now use the definition of magnetic moment

Answer 40

magnetic moment=iA
=[ev/2(pi)r]A

Answer 41

yeah, and what is A for a circle of radius r?

Answer 42

\[\Pi r ^{2}\]

Answer 43

ok, so now plug that in...

Answer 44

\[\mu = \frac{ ev }{ 2 \pi r} \pi r ^{2}\]

Answer 45

\[\mu =\frac{ evr }{2}\]

Answer 46

great, do you see what to do now? one last step....

Answer 47

\[\mu = \frac{ e }{ 2m} mvr\]

Answer 48

yes i got it..but now what the expression shows..i mean what would be its physical significance?

Answer 49

it means that if you have an electron orbiting in a circular Bhor-like atom you have an associated magnetic dipole field

Answer 50

what would be the case if it is spinning?

Answer 51

electrons can't spin about their own axis because they don't have one