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Magnetism and conservation of energy

  1. Jul 24, 2010 #1
    Hello Guys

    I am a new joinee and this is my first question. I apologise if the question is little trivial. Basically, Think of the following:

    Scenario: There is a strong bar magnet and some magnetic metal balls lying on the floor of a room.

    Step 1: I lift the magnet from the floor and hold it in my hand. I hold it to a certain height

    Step2. I use the magnet from that height (if necessary, moving it in the horizontal plane) to lift a ball. Basically the ball is lifted by the attractive force (assuming it is a sufficiently strong magnet) of the magnet. Now this ball has acquired some potential energy (compared to the floor), depending on its mass m and the height h.

    Step3. I repeat step2 for other balls lying on the floor.

    Conclusion: We can conclude that the magnetic force of the bar magnet did the work to lift each ball which resulted in the corresponding gain in potential energy.

    Question: Now, my question is : In terms of conservation of energy, how do you explain this? I mean, there are some gain in energy (of these balls), but where is the corresponding loss to account for the conservation of energy? Have we not, even if very slightly, increased the total energy of the whole universe?
  2. jcsd
  3. Jul 24, 2010 #2
    Good one!

    The answer as always is you have to look at the larger picture.

    When the magnet was made, a lot of energy had to be expended to create it's magnetic field. That energy is not lost, it's stored in the magnet's field.

    When you use that energy to lift your balls, the field energy is diminished slightly (the magnet is not quite as strong now).
    When you remove the balls, the energy is returned to the field (magnet regains it's strength).
  4. Jul 25, 2010 #3
    Many thanks, AJ. I think I got my explanations
  5. Jul 25, 2010 #4
    Consider that potential energy isn't only due to gravitational force. There is a difference in potential energy between a relaxed spring and one that is compressed or stretched, and there is a difference in potential energy between a ferrous object and a magnet (or two magnets) at any two distances from each other.

    You can extract work from a pair of magnets falling toward each other, but will have to put in the same amount of work to move them back apart from each other. If one magnet is lifting the other in a gravity field, the difference in gravitational potential energy is subtracted from the magnetic potential energy available to perform work. The excess energy is dissipated in the collision as noise and heat, and a tiny amount as electromagnetic radiation due to the shifting magnetic fields. Overall, energy is still conserved.
  6. Jul 25, 2010 #5
    I used to have this same question when I was in highschool but I figured it out quickly.

    Its trivial, there is a potential relative to the magnet, so there is no contradiction wit conservation of energy. This is why the process is not repeatable.
  7. Jul 26, 2010 #6
    The gain in the gravitational potential energy of the balls is offset by the loss in magnetic potential energy between the balls and the magnet.

    (The magnetic potential energy between the balls and the magnetic is lowered as the balls get closer to the magnet....and energy is required to seperate them).

  8. Jul 26, 2010 #7


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    Defining potential of metal balls relative to the magnet is a clumsy way of doing things. Look at the energy of magnetic field instead.
  9. Jul 26, 2010 #8
    Ahh... but work was required to place these items in position to create the effect.
    Thus, all is conserved.
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