Calculating the total energy available from a permanent magnet involves understanding the energy contained in its magnetic fields and the implications of energy extraction. The energy exerted by a magnet decreases as energy is drawn from its field, affecting the strength of the magnetic force. Since magnetic fields are conservative, energy used to attract objects like pins is returned when those objects are moved away, complicating energy extraction. The challenge lies in efficiently accessing this energy without being limited by the decreasing field strength as distance increases. Overall, the energy within a magnet's field is localized and difficult to fully utilize.
#1
Shantaram
3
0
Does anyone know how to calculate the total energy of magnet?
Thanks!
Does anyone know how to calculate the total energy of magnet?
Thanks!
Welcome to the PF. What is the context of your question? Is it a school question, a school project, or for personal interest? What do you know about magnets and energy so far? Do you mean the energy required to initially magnetize a permanent magnet, or the energy available from a permanent magnet to do work on something? What kind of something?
#3
Shantaram
3
0
Thanks for reply.
Its my personal interest to know about the permanent magnet.
I meant,total energy avilable from the magnet to do some work.
Probably the best way to do it is to calculate the energy contained in the magnetic fields created by the magnet. But that is probably not the same as the total energy available. It is an interesting question to ponder about whether or not we could actually extract all the energy from a magnet through its magnetic field interactions. This is because the force exerted is proportional to the field strength. As we extract energy from the magnetic fields, their strength must decrease to reflect the appropriate reduction in the energy density of the fields. Thus, the amount of mass that can be moved decreases since we have to overcome such environmental forces as gravity or friction.
EDIT: Not only that but a magnet field is conservative. If I use a magnet to draw close a pin, it exerts force and expends energy. However, if I take the pin and move back to its original position, I give back the same energy to the magnetic field. So now we have a problem, let's say we have millions of these pins and we want to extract all the energy by having the magnet pull in these pins. But we cannot clear away the pins after they are pulled in since this returns energy to the magnet. So now the pins have to pile up on th magnet, this means that the next pin can only be pulled in over a smaller and smaller distance. And the farther we go away from the magnet, the weaker the field is. So the energy in the fields is locked in locally to the magnet. It is another problem to get at this energy without being forced to use objects to heavy to pull in and too low in density to pull in a large number to a close proximity.
#5
Shantaram
3
0
Thanks!
Yes, you are right.The magnetic field is change with respect to varying airgap between poles.
can I get any brief information on this?
Susskind (in The Theoretical Minimum, volume 1, pages 203-205) writes the Lagrangian for the magnetic field as ##L=\frac m 2(\dot x^2+\dot y^2 + \dot z^2)+ \frac e c (\dot x A_x +\dot y A_y +\dot z A_z)## and then calculates ##\dot p_x =ma_x + \frac e c \frac d {dt} A_x=ma_x + \frac e c(\frac {\partial A_x} {\partial x}\dot x + \frac {\partial A_x} {\partial y}\dot y + \frac {\partial A_x} {\partial z}\dot z)##.
I have problems with the last step. I might have written ##\frac {dA_x} {dt}...
I am reading the Griffith, Electrodynamics book, 4th edition, Example 4.8. I want to understand some issues more correctly. It's a little bit difficult to understand now.
> Example 4.8. Suppose the entire region below the plane ##z=0## in Fig. 4.28 is filled with uniform linear dielectric material of susceptibility ##\chi_e##. Calculate the force on a point charge ##q## situated a distance ##d## above the origin.
In the page 196, in the first paragraph, the author argues as follows ...