The Electromagnetic Pump. Magnetic forces acting on...

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 $l = 35.0 \mathrm { mm } ?$

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 $l = 35.0 \mathrm { mm } ?$

Key Concepts

Lorentz Force

The Lorentz force is the fundamental principle describing the force experienced by a charged particle or a current-carrying conductor in the presence of a magnetic field. In a fluid, the interaction of an electric current (characterized by current density) and a magnetic field generates a force per unit volume, which is essential in the operation of electromagnetic pumps.

Electromagnetic Pumping

Electromagnetic pumping refers to the method of moving a conducting fluid by utilizing the Lorentz force generated from the interaction between an applied magnetic field and an electric current. This technique avoids mechanical contact, making it ideal for fluids that may be sensitive or delicate, such as biological fluids.

Current Density

Current density is defined as the electric current per unit cross-sectional area of a conductor. In the context of electromagnetic pumping, it determines the magnitude of the Lorentz force when interacting with a magnetic field, thereby directly influencing the induced pressure gradient in the fluid.

Magnetic Field Interaction with Conducting Fluids

A magnetic field exerts a directional force on moving charges within a conducting fluid. When combined with an applied current, this interaction produces a uniform force distribution that can create a pressure differential, serving as the operative mechanism behind electromagnetic pumps.

Pressure Gradient Generation

The pressure gradient in a conducting fluid, generated by the Lorentz force, is a key concept in fluid dynamics. This gradient is the result of the force acting on the fluid elements, allowing for the controlled pumping or movement of the fluid without mechanical parts.

Please give Ace some feedback