English: Diagram showing the forces on an
electron in a metal sheet moving to the right under a magnet
![{\displaystyle \mathbf {N} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/c2f63b6cd6d63ee9b7be0b7e4d14099d7153bd43)
, explaining
eddy currents, and where the drag force on the sheet comes from. The red dot
![{\displaystyle \mathbf {e} _{\text{1}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/66e689b14d7dc8bc9592c4acfdaadbd6fc4ddf1f)
shows an electron in the metal under the magnet right after it has undergone a collision, and
![{\displaystyle \mathbf {e} _{\text{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/65b0a74a3ca2ad6eca0a97ad3ef5b62bf3681648)
shows the same electron after it has been accelerated by the magnetic field. On average at
![{\displaystyle \mathbf {e} _{\text{1}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/66e689b14d7dc8bc9592c4acfdaadbd6fc4ddf1f)
the electron has the same velocity as the sheet
(black arrow). in the
![{\displaystyle +\mathbf {x} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/54c722029f50f473e7b166a1cf2d689f4960d182)
direction. The magnetic field (
![{\displaystyle \mathbf {B} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/cafb0ef39b0f5ffa23c170aa7f7b4e718327c4d1)
,
green arrow) of the magnet's North pole N is directed down in the
![{\displaystyle -\mathbf {y} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/29502381c2d9b0ffcfc7cca4a0db68f77bafaf6a)
direction. The magnetic field exerts a
Lorentz force on the electron
(pink arrow) of
![{\displaystyle \mathbf {F} _{\text{1}}=-e(\mathbf {v} \times \mathbf {B} )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b2a3963737a376e4db2e392e6766763886e3cb47)
, where
e is the electron's charge. Since the electron has a negative charge, from the
right hand rule this is directed in the
![{\displaystyle +\mathbf {y} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/41216c18cd1496a09a8fe3b09917f5e55b2e153f)
direction. At
![{\displaystyle \mathbf {e} _{\text{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/65b0a74a3ca2ad6eca0a97ad3ef5b62bf3681648)
this force gives the electron a component of velocity in the sideways direction (
![{\displaystyle \mathbf {v} _{\text{2}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eb310cc9f48a386eb16f8c6cf0db7d928e7f2615)
.
black arrow) The magnetic field acting on this sideways velocity, then exerts a Lorentz force on the particle of
![{\displaystyle \mathbf {F} _{\text{2}}=-e(\mathbf {v} _{\text{2}}\times \mathbf {B} )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ea408b4fbfeb67de61c72659299a11331f446144)
. From the right hand rule, this is directed in the
![{\displaystyle -\mathbf {x} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/f0a01370ff50ffc54518e7c4c1199279b0370f68)
, opposite to the velocity
![{\displaystyle \mathbf {v} }](https://wikimedia.org/api/rest_v1/media/math/render/svg/35c1866e359fbfd2e0f606c725ba5cc37a5195d6)
of the metal sheet. This force accelerates the electron giving it a component of velocity opposite to the sheet. Collisions of these electrons with the atoms of the sheet exert a drag force on the sheet.