A hall probe used to measure magnetic field strengths consistsofa rectangular slab of material (free-electron density n) withwidthd and thickness t , carrying a current I along its lengthl.the slabis immersed in a magnetic field of magnitude Borientedperpendicular to its rectangular face (of area l d ), sothat ahall emf &H is produced across its with d. theprobeâsmagnetic sensitivity , defind as KH = &H /l B ,indicates themagnitude of the hall emf achieved for a given appliedmagneticfield and current. A slab with a large KH is a goodcandidate foruse as a Hall probe. (a) Show that KH =1/ent. Thus, agood Hallprob has small values for both n and t .(b)as possiblecandidatesfor the material used in a Hall probe, consider (i)atypical metal(n=1*(10^29)/m^3)and (ii)a (doped)semiconductor(jn=3*(10^23)/m^3). Given that a semiconductor slabcan bemanufactured with a thickness of 0.15mm, how thin (nm) shouldametal slab be yield a KH value equal to that of thesemiconductorslab? Compare this metal slab thickness with the0.3-nm size of atypical metal atom.(c) for the typicalsemiconductor slab described in part (b), what is the expectedvalue for &Hwhen I = 100 mA and B=0.1 T?
A hall probe used to measure magnetic field strengths consistsofa rectangular slab of material (free-electron density n) withwidthd and thickness t , carrying a current I along its lengthl.the slabis immersed in a magnetic field of magnitude Borientedperpendicular to its rectangular face (of area l d ), sothat ahall emf &H is produced across its with d. theprobeâsmagnetic sensitivity , defind as KH = &H /l B ,indicates themagnitude of the hall emf achieved for a given appliedmagneticfield and current. A slab with a large KH is a goodcandidate foruse as a Hall probe. (a) Show that KH =1/ent. Thus, agood Hallprob has small values for both n and t .(b)as possiblecandidatesfor the material used in a Hall probe, consider (i)atypical metal(n=1*(10^29)/m^3)and (ii)a (doped)semiconductor(jn=3*(10^23)/m^3). Given that a semiconductor slabcan bemanufactured with a thickness of 0.15mm, how thin (nm) shouldametal slab be yield a KH value equal to that of thesemiconductorslab? Compare this metal slab thickness with the0.3-nm size of atypical metal atom.(c) for the typicalsemiconductor slab described in part (b), what is the expectedvalue for &Hwhen I = 100 mA and B=0.1 T?
