Variation of the Strength of a Magnetic field?

[pete94857]

TL;DR Summary

With distance from the source the feild strength is reduced. Do the electrons travel slower the further from the source ? And thus faster closer to the source. Or is the feild strength reduced simply because there are less electrons but the speed of them is the same as inner feild. I'm asking because I'm Trying to figure out the force of something travelling through the feild. Does the force accumulate. Or does the weaker points slow things. For example opposing magnets moving away freely ?

With distance from the source the feild strength is reduced. Do the electrons travel slower the further from the source ? And thus faster closer to the source. Or is the feild strength reduced simply because there are less electrons but the speed of them is the same as inner feild. I'm asking because I'm Trying to figure out the force of something travelling through the feild. Does the force accumulate. Or does the weaker points slow things. For example opposing magnets moving away freely from each other ? Do I accumulate the force , subtract the force or find an average over the distance. ?

 

[kuruman]

What electrons? What is the picture in your mind about two magnets repelling each other?

 

[pete94857]

The electrons from the magnetic field. Say any 2 permanent magnets repelling each other. Or is it the same as dropping something off a cliff either vertically down or onto a slope. The energy is the same but divided into the slope. I don't know.

 

[pete94857]

After further contemplation to try and answer my own question. There's no reason why the reduced force in the outer field would cause a slowing. The best way to calculate it would be to break the distance into smaller section, the more the better then draw an average over each section I.e 10 kgf at 0 distance 5 kgf at 1 average of 7.5 kgf convert to Newtons x 9.8 and times the distance of that section to get the kinetic energy repeat for all sections then add up the total from each section.

 

[kuruman]

The electrons from the magnetic field.

There is no such thing. Permanent magnets do not emit electrons.

Here is a very simplified explanation of magntism in matter. . An electron has a magnetic moment that, together with mass and charge, is part and parcel of what makes it an electron. Having a magnetic moment means that an electron can be viewed as a teeny tiny bar magnet. Now a small block of matter contains a prodigious number of electrons in them of the order of 10,000.000,000,000,000,000,000,000.

The reason that a piece of non-magnetic material like wood is not attracted or repelled by permanent magnet is that the tiny electron magnets in the wood are frozen in random directions. So when a permanent magnet is brought near them some are attracted and some are repelled, the net force being zero.

In a permanent magnet, the tiny electron magnets in it are all permanently aligned more or less in the same direction and add up to give a huge net non-zero magnetic field. When two permanent magnets are brought together, they either attract or repel each other depending on their relative orientation. Both attraction and repulsion are ways to minimize the potential energy of the configuration. This is analogous to a rock released from rest near the surface of the Earth. It moves closer to the center of the Earth in order to minimize the gravitational potential energy of the configuration.

To complete the picture, there is the special category of ferromagnetic materials, soft iron for example, in which the electron magnetic moments are initially oriented randomly like in the piece of wood. Two pieces of iron do not normally attract each other. However if you bring a permanent magnet near a piece of soft iron, there will be attraction regardless of whether the south or north pole is closer to the iron. The picture here is that the orientation of the magnetic moments in the iron is not frozen. The moment can rotate like compass needles so their north/south pole is closer to the south/north pole of the permanent magnet. This means that the force between the two is always attractive and never repulsive. As to why the magnetic moments rotate and are attracted, it is also to minimize the potential energy of the configuration.

The subject of magnetism in matter is vast and complex so I stop here.

 

[kuruman]

After further contemplation to try and answer my own question. There's no reason why the reduced force in the outer field would cause a slowing. The best way to calculate it would be to break the distance into smaller section, the more the better then draw an average over each section I.e 10 kgf at 0 distance 5 kgf at 1 average of 7.5 kgf convert to Newtons x 9.8 and times the distance of that section to get the kinetic energy repeat for all sections then add up the total from each section.

The best way would be to model the problem mathematically as I attempted to do for you in the other thread that you started. However, it requires understanding of calculus and the understanding that force varies with distance. It's not clear what you mean by "drawing an average over each section". If the value of the force is $F_1$ at the beginning of a section you also need to know the value $F_2$ at the end of the section in order to take an average. How do you figure out the value of $F_2$ if you don't know how the force varies with distance?

 

[pete94857]

The best way would be to model the problem mathematically as I attempted to do for you in the other thread that you started. However, it requires understanding of calculus and the understanding that force varies with distance. It's not clear what you mean by "drawing an average over each section". If the value of the force is $F_1$ at the beginning of a section you also need to know the value $F_2$ at the end of the section in order to take an average. How do you figure out the value of $F_2$ if you don't know how the force varies with distance?

I understand the best way would probably be with advanced mathematical equations unfortunately I don't have that experience or knowledge. What I meant regarding drawing an average was to either measure the feild manually over the distance at various points or take already known information from another source. I'd be grateful if you could clarify would the feild reduce according to the inverse square law or inverse cube law or both depending on the distance or some other law ?

 

[kuruman]

If you can make measurements, that would be good. As a I mentioned in the other thread, you can approximate the field as dipolar which varies as the inverse cube of the axial distance. Draw a line and orient the magnet so that the north-south pole line segment is on that line. Call that the $z$-axis. The magnetic field points away from the magnet on the north pole side of the axis and towards the magnet on the south pole side of the axis. In other words, the magnetic field points in the same direction everywhere on the axis. Now the value of the magnetic field on the axis depends, in the dipole approximation, as the inverse cube of the distance from the center of the magnet. This means that you can write the size of field at distance $z$ from the magnet as $$B=\frac{A}{z^3}$$ where $A$ is some constant that you can determine by measurement.

To do that, you can measure the field at distance $z_0$ and say the value you get is $B_0$. Then, according to the equation above, $B_0=\frac{A}{z_0^3}$ and this can be solved to find the constant $A$, $A=B_0~z_0^3$ in which case you can write $$B=\frac{B_0z_0^3}{z^3}=B_0\left(\frac{z_0}{z}\right)^3.$$Note that this expression allows you to find the field at any axial distance $z$ from the magnet if you know the value at one point. However, you need to remember that this is an approximation. You may wish to make additional measurements at other distances and see how close the approximation to what is actually the case.