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 \(l\) is in the field (Fig.
P27.90). The tube is filled with a
conducting liquid, and an electric current of density \(J\) is maintained in the
third mutually perpendicular direction. (a) Show that the difference of
pressure between a
point in the liquid on a vertical plane through \(a b\) and a point in the
liquid on another vertical plane through \(c d ,\) under conditions in
which the liquid is prevented from flowing, is \(\Delta p = J / B\) . (b) What
current density is needed to provide a pressure difference of 1.00 atm
between these two points if \(B = 2.20 \mathrm { T }\) and \(l = 35.0 \mathrm {
mm } ?\)
