Force on a Magnet in Lenz's Law

Hesch
Gold Member
ΔE is the change in total energy. It could be written:

F = ΔEtotal / Δs

Etotal = Emagn * V, as Emagn is not an energy, but an energy density. It emerges from:

F = ΔE / Δs = ( Emagn * ΔV ) / Δs = Emagn * A. ( s is distance, A is cross section area of field, V is volume of field ).

andrevdh
Homework Helper
Ok. Lets say we move a little distance Δs in the field.
There is a change in the amount of energy in the field equal to E2 - E1.
To calculate this we use the magnetic energy densities at points s1 and s2 : (Em2 - Em1 )* ΔV
where Em is the magnetic energy per unit volume.
What does the ΔV signify? We are calculating the magnetic energy difference a little distance apart in the field. What volume, ΔV, should be used for
this calculation? Thank you for your patience with me. It usually takes me several days to understand something.

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Hesch
Gold Member
The magnetic energy density will be about constant, as the induced current in the loop will substitute the disappearing B-field, when the magnet is gradually removed.
Thus E2 - E1 = Emagn * ΔV.

Of course that is not the truth when moving the magnet some 2 meters away, but nearby it's the truth.

andrevdh
Homework Helper
We have moved a little distance Δs in the field.
The energy difference at the end and the beginning in the field is the product of the magnetic energy density and a small volume.
This product will tell us what the amount of energy is in such a small volume and not the difference in energy at the start and
end of the Δs movement.

Hesch
Gold Member
This product will tell us what the amount of energy is in such a small volume and not the difference in energy at the start and
end of the Δs movement.
Thus E2 - E1 = Emagn * ΔV.

andrevdh
Homework Helper
No the product Emagn*ΔV gives you the amount of magnetic energy in the small volume
and not the difference in energy. Emagn is the amount of magnetic energy in one unit of volume.

Hesch
Gold Member
Emagn has the unit [ J/m3 ]

ΔV has the unit [ m3 ]

Thus

E2 - E1 = Emagn * ΔV

has the unit [ J ]. Why do you continue this discussion ?

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