28. Magnetic Fields and Forces

A 150-V battery is connected across two parallel metal plates of area 28.5 cm^2 and separation 8.20 mm. A beam of alpha particles (charge +2e, mass 6.64x10^-27 kg) is accelerated from rest through a potential difference of 1.75 kV and enters the region between the plates perpendicular to the electric field, as shown in Fig. E27.29 <IMAGE>. What magnitude and direction of magnetic field are needed so that the alpha particles emerge undeflected from between the plates?

(III) The Hall effect can be used to measure blood flow speed because the blood contains ions that constitute an electric current. (a) Does the sign of the ions influence the emf? Explain. (b) Determine the flow speed in an artery 3.3 mm in diameter if the measured emf across the width of the artery is 0.13 mV and B is 0.070 T. (In actual practice, an alternating magnetic field is used.)

(II) A long copper strip is 3.0 cm wide and thick. When it carries a steady 42-A current in a 0.80-T magnetic field it produces a 6.5-μV Hall emf. Determine: (a) the Hall field in the conductor; (b) the drift speed of the conduction electrons; (c) the density of free electrons in the metal.

(II) A Hall probe, consisting of a rectangular slab of current-carrying material, is calibrated by placing it in a known magnetic field of magnitude 0.10 T. When the field is oriented normal to the slab’s rectangular face, a Hall emf of 12 mV is measured across the slab’s width. The probe is then placed in a magnetic field of unknown magnitude B, and a Hall emf of 63 mV is measured. Determine B assuming that the angle θ between the unknown field and the plane of the slab’s rectangular face is (a) θ = 90°, and (b) θ = 60°.