3. The Electromagnetic Pump.Magneticþnductingonvenient means of pumping thesefluids. For example, this methodcan be used to pump blood withoutthe damage to the cells that can becaused by a mechanical pump. Ahorizontal tube with rectangularcross section (height h, width w) is kplaced at right angles to a uniformmagnetic field with magnitude B soactingprovideforcesonfluidsа`Liquid metalor bloodthatlength is in the field. The tube is filled with aconducting liquid, and an electric current of density J ismaintained in the third mutually perpendicular direction.Show that the difference of pressure between a point in theliquid on a vertical plane through ab and a point in the liquidon another vertical plane through cd, under conditions inwhich the liquid is prevented from flowing, is .

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nillan Learning Activity on the Sun, such as solar flares and coronal mass ejections, hurls large numbers of charged particles into space. When the particles reach Earth, they can interfere with communications and the power grid by causing electromagnetic induction. For example, a current of millions of amps (known as the auroral electrojet) that runs approximately 100 km above Earth's surface can be perturbed. The change in the current causes a change in the magnetic field it produces at Earth's surface, which induces an emf along Earth's surface and in the power grid (which is grounded). Induced electric fields as high as 6.0 V/km have been measured. We can model the circuit at Earth's surface as a rectangular loop made up of the power lines completed by a path through the ground beneath. We can treat the magnetic field created by the electrojet as being uniform (but not constant) and parallel to Earth's surface near the surface. Consider a 1.0-km-long stretch of power line that is…
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