Question: In a Wien velocity filter, perpendicular electric and magnetic fields are applied to moving charges so that only those charges with velocity v = E/B pass through the fields without deflection. Figure illustrates a complementary situation: charged particles moving through a conducting material (such as electrons moving through a copper wire) are confined by the walls of the conductor so that they move in straight lines parallel to the axis of the conductor. A magnetic field applied perpendicular to the motion causes the moving negative charges to separate from positive charge and produce an electric field within the conductor, perpendicular to the current, that offsets the magnetic force and keeps the charges moving in straight lines along the conductor. This induced electric field is called the Hall Effect. (Because blood is a conducting fluid, surgeons can measure blood flow rates using the Hall Effect.)
a. The figure shows electrons moving along a long wire. What is the direction of the electric field E within the wire? (Make a sketch.)
b. Suppose the wire has a square cross section with width and height equal to 1 cm. If the velocity of the charges is 5 mms-1, and B = 2.0 T, what potential difference would appear across the wire? This potential difference can be measured with a voltmeter.
c. If you measure current with an ammeter, you cannot distinguish between positive charges flowing through the meter in one direction, and negative charges flowing in the opposite sense. But the Hall Effect allows you to determine both the polarity and the direction of motion of the charges. Explain this: imagine positive charges moving opposite to the direction shown in the figure. What happens to the induced E field?
Fig. - The half effect on charged particles moving through a conductor.