Figure E27.53 shows a Figure E27.53 portion of a silver ribbon with 11.8 mm and

Question

Figure E27.53 shows a Figure E27.53 portion of a silver ribbon with 11.8 mm and yi 0.23 mm, carrying a current of 120 A in the x-direction. The ribbon lies in a uniform magnetic field, in the y direction. with magnitude 0.95 T. Apply the sim- plified model of the Hall effect presented in Section 27.9. If there are 5.85 x 10 free electrons per cubic meter, find (a) the 28 magnitude of the drift velocity of the electrons in the x-direction; (b) the magnitude and direction of the electric field in the z-direction due to the Hall effect; (c) the Hall emf

Explanation / Answer

given,

magnitic field B=0.95 T

z1= 11.8 mm

y1= 0.23 mm

current i= 120 A

density of free electrons n=5.85*10^28 /m^3

a)

drift velocity, Vd=i/A*n*e

Vd = i/A*n*e

= 120/((11.8*0.23*10^-6)*(5.85*10^28)*(1.6*10^-19))

= 4.72*10^-3 m/sec

= 4.72 mm/sec

b)

E=Vd*B

= 4.72*10^-3*0.95

= 4.484 mT

direction of E is along z-axis

c)

Hall voltage

VH = E/d

= E/z1

= (4.484*10^-3)/(11.8*10^-3)

VH = 0.38 v

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