 # Essay On The Hall Effect

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The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current. The forces acting on the moving charges in a conductor in a magnetic field is strikingly demonstrated by the Hall effect, an effect analogous to the transverse deflection of an electron beam in a magnetic field in vacuum. (The effect was discoveredby the American physicist Edwin Hall in 1879 while he was still a graduate student.) To describe this effect, let’s consider a conductor in the form of a flat strip. The current is in the direction of the +x-axis, and there is a uniform magnetic field B perpendicular to the plane of the strip,…show more content…
T10.1b shows positive charges. In both cases the magnetic force is upward, just as the magnetic force on a conductor is the same whether the moving charges are positive or negative. In either case a moving charge is driven toward the upper edge of the strip by the magnetic force Fz = |q|vdB. If the charge carriers are electrons, an excess negative charge accumulates at the upper edge of the strip, leaving an excess positive charge at its lower edge. This accumulation continues until the resulting transverse electrostatic field E becomes large enough to cause a force (magnitude |q|E) that is equal and opposite to the magnetic force (magnitude |q|vd B). After that, there is no longer any net transverse force to deflect the moving charges. This electric field causes a transverse potential difference between opposite edges of the strip, called the Hall voltage or the Hall emf. The polarity depends on whether the moving charges are positive or negative. Experiments show that for metals the upper edge of the strip in Fig. T10.1a does become negatively charged, showing that the charge carriers in a metal are indeed negative…show more content…
These materials conduct by a process known as hole conduction. Within such a material there are locations, called holes, that would normally be occupied by an electron but are actually empty. A missing negative charge is equivalent to a positive charge. When an electron moves in one direction to fill a hole, it leaves another hole behind it. The hole migrates in the direction opposite to that of the electron. In terms of the coordinate axes in Fig. T10.1b, the electrostatic field E for the positive-q case is in the −z-direction; its z-component Ez is negative. The magnetic field is in the +y-direction, and we write it as By . The magnetic force (in the +zdirection) is qvd By. The current density Jx is in the +x-direction. In the steady state, when the forces qEz and qvdBy are equal in magnitude and opposite in direction, This confirms that when q is positive, Ez is negative. The current density Jx is Eliminating vd between these equations, we find (T10.1) Note that this result (as well as the entire derivation) is valid for both positive and negative q. When q is negative, Ez is positive, and conversely. We can measure Jx , By , and Ez, so we can compute the product nq. In both metals and semiconductors, q is equal in magnitude to the electron charge, so