The Electromagnetic Pump. Magnetic forces acting on conducting fluids provide a convenient means of pumping these fluids. For example, this method can be used to pump blood without the damage to the cells that can be caused by a mechanical pump. A horizontal tube with rectangular cross section (height h, width w) is placed at right angles to a uniform magnetic field with magnitude B so that a length e is in the field. The tube is filled with a conducting liquid, and an electric current of density J is maintained in the third mutually perpendicular direction. Show that the difference of pressure between a point in the liquid on a vertical plane through ab and a point in the liquid on another vertical plane through cd, under conditions in which the liquid is prevented from flowing, is Ap = JeB. `Liquid metal or blood

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Need detailed solution with using vectors.

The Electromagnetic Pump. Magnetic forces acting on conducting
fluids provide a convenient means of pumping these fluids. For example,
this method can be used to pump blood without the damage to the cells
that can be caused by a mechanical pump. A horizontal tube with
rectangular cross section (height h, width w) is placed at right angles to
a uniform magnetic field with magnitude B so that a length e is in the
field. The tube is filled with a conducting liquid, and an electric current of
density J is maintained in the third mutually perpendicular direction.
Show that the difference of pressure between a point in the liquid on a
vertical plane through ab and a point in the liquid on another vertical
plane through cd, under conditions in which the liquid is prevented from
flowing, is Ap = JeB.
`Liquid metal
or blood

Image Transcription

The Electromagnetic Pump. Magnetic forces acting on conducting fluids provide a convenient means of pumping these fluids. For example, this method can be used to pump blood without the damage to the cells that can be caused by a mechanical pump. A horizontal tube with rectangular cross section (height h, width w) is placed at right angles to a uniform magnetic field with magnitude B so that a length e is in the field. The tube is filled with a conducting liquid, and an electric current of density J is maintained in the third mutually perpendicular direction. Show that the difference of pressure between a point in the liquid on a vertical plane through ab and a point in the liquid on another vertical plane through cd, under conditions in which the liquid is prevented from flowing, is Ap = JeB. `Liquid metal or blood

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