In a Hall experiment consider a rectangular semiconductor sample with length L,

Question

In a Hall experiment consider a rectangular semiconductor sample with length L, width W, and thickness D. The sample carries a current I across the cross-sectional area WxD along L, in the positive x direction. The face WxL is exposed to a magnetic field B, which is in the positive y-direction. A voltmeter is connected across the width. If the charge carriers are positively charged holes and their concentration is N, in which direction is:

a) drift velocity

b)cross produdt of velocity and magnetic field

c)Lorenz magnetic force

d)Hall electric field

e)Calculate the Hall voltage

f) which of these vectors would change the direction if the charge carriers were not holes but electrons?

Explanation / Answer

a. Drift Velocity is given by the expression Vd = i/NeA

where i is current, N is no. of ELelcrns

e is charge 1.6 e -19 C and A is Area

so its direction will be along the x to direction

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b. Cross Product of Velocity and magnetic field B gives ELectric filed

as E = v x B

so direction of ELecric field wll be Y direction

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Lorenttz force is given by F = Eq + qVB

directio will be Upwards

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HAll Electric filed is along x direction

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HAll VOlatge is given by the formula

Vh =   iBD/(neWXD)

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electric field , Lorentz force, magnetic field,wll change their directions upon changing the CHarge carriers

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